Deck 10: Extension H: Vector Functions

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Find the velocity and position vectors of an object with acceleration Find the velocity and position vectors of an object with acceleration   initial velocity   and initial position  <div style=padding-top: 35px> initial velocity Find the velocity and position vectors of an object with acceleration   initial velocity   and initial position  <div style=padding-top: 35px> and initial position Find the velocity and position vectors of an object with acceleration   initial velocity   and initial position  <div style=padding-top: 35px>
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Question
Find the scalar tangential and normal components of acceleration of a particle with position vector <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>

A) <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
B) <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
C) <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
D) <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
Question
Find the velocity,acceleration,and speed of an object with position function Find the velocity,acceleration,and speed of an object with position function   for   Sketch the path of the object and its velocity and acceleration vectors. <div style=padding-top: 35px> for Find the velocity,acceleration,and speed of an object with position function   for   Sketch the path of the object and its velocity and acceleration vectors. <div style=padding-top: 35px> Sketch the path of the object and its velocity and acceleration vectors.
Question
Find the velocity,acceleration,and speed of an object with position function Find the velocity,acceleration,and speed of an object with position function   for   Sketch the path of the object and its velocity and acceleration vectors. <div style=padding-top: 35px> for Find the velocity,acceleration,and speed of an object with position function   for   Sketch the path of the object and its velocity and acceleration vectors. <div style=padding-top: 35px> Sketch the path of the object and its velocity and acceleration vectors.
Question
Find the acceleration of a particle with the following position function. <strong>Find the acceleration of a particle with the following position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the acceleration of a particle with the following position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the acceleration of a particle with the following position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the acceleration of a particle with the following position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the acceleration of a particle with the following position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the acceleration of a particle with the following position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the speed of a particle with the given position function. <strong>Find the speed of a particle with the given position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the speed of a particle with the given position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the speed of a particle with the given position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the speed of a particle with the given position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the speed of a particle with the given position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the speed of a particle with the given position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the velocity of a particle that has the given acceleration and the given initial velocity.
<strong>Find the velocity of a particle that has the given acceleration and the given initial velocity.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the velocity of a particle that has the given acceleration and the given initial velocity.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the velocity of a particle that has the given acceleration and the given initial velocity.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the velocity of a particle that has the given acceleration and the given initial velocity.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the velocity of a particle that has the given acceleration and the given initial velocity.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the velocity of a particle that has the given acceleration and the given initial velocity.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the acceleration of a particle with the given position function. <strong>Find the acceleration of a particle with the given position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the acceleration of a particle with the given position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the acceleration of a particle with the given position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the acceleration of a particle with the given position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the acceleration of a particle with the given position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the acceleration of a particle with the given position function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the velocity,acceleration,and speed of an object with position function Find the velocity,acceleration,and speed of an object with position function   for   Sketch the path of the object and its velocity and acceleration vectors. <div style=padding-top: 35px> for Find the velocity,acceleration,and speed of an object with position function   for   Sketch the path of the object and its velocity and acceleration vectors. <div style=padding-top: 35px> Sketch the path of the object and its velocity and acceleration vectors.
Question
The position function of a particle is given by
<strong>The position function of a particle is given by   When is the speed a minimum?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
When is the speed a minimum?

A) <strong>The position function of a particle is given by   When is the speed a minimum?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>The position function of a particle is given by   When is the speed a minimum?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>The position function of a particle is given by   When is the speed a minimum?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>The position function of a particle is given by   When is the speed a minimum?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>The position function of a particle is given by   When is the speed a minimum?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
A projectile is fired from ground level with an initial speed of 1100 ft/sec and an angle of elevation of <strong>A projectile is fired from ground level with an initial speed of 1100 ft/sec and an angle of elevation of   </strong> A) Find the range of the projectile. B) What is the maximm height attained by the projectile? C) What is the speed of the projectile at impact? Round your answers to the nearest integer. <div style=padding-top: 35px>

A) Find the range of the projectile.
B) What is the maximm height attained by the projectile?
C) What is the speed of the projectile at impact?
Round your answers to the nearest integer.
Question
A ball is thrown at an angle of <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> to the ground.If the ball lands <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> m away,what was the initial speed of the ball? Let <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the scalar tangential and normal components of acceleration of a particle with position vector Find the scalar tangential and normal components of acceleration of a particle with position vector   <div style=padding-top: 35px>
Question
A force with magnitude <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   <div style=padding-top: 35px> N acts directly upward from the xy-plane on an object with mass <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   <div style=padding-top: 35px> kg.The object starts at the origin with initial velocity <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   <div style=padding-top: 35px> Find its position function.

A) <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   <div style=padding-top: 35px> <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   <div style=padding-top: 35px> <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   <div style=padding-top: 35px>
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Deck 10: Extension H: Vector Functions
1
Find the velocity and position vectors of an object with acceleration Find the velocity and position vectors of an object with acceleration   initial velocity   and initial position  initial velocity Find the velocity and position vectors of an object with acceleration   initial velocity   and initial position  and initial position Find the velocity and position vectors of an object with acceleration   initial velocity   and initial position
2
Find the scalar tangential and normal components of acceleration of a particle with position vector <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)

A) <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)     <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)
B) <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)     <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)
C) <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)     <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)
D) <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)     <strong>Find the scalar tangential and normal components of acceleration of a particle with position vector  </strong> A)     B)     C)     D)
3
Find the velocity,acceleration,and speed of an object with position function Find the velocity,acceleration,and speed of an object with position function   for   Sketch the path of the object and its velocity and acceleration vectors. for Find the velocity,acceleration,and speed of an object with position function   for   Sketch the path of the object and its velocity and acceleration vectors. Sketch the path of the object and its velocity and acceleration vectors.
4
Find the velocity,acceleration,and speed of an object with position function Find the velocity,acceleration,and speed of an object with position function   for   Sketch the path of the object and its velocity and acceleration vectors. for Find the velocity,acceleration,and speed of an object with position function   for   Sketch the path of the object and its velocity and acceleration vectors. Sketch the path of the object and its velocity and acceleration vectors.
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5
Find the acceleration of a particle with the following position function. <strong>Find the acceleration of a particle with the following position function.  </strong> A)   B)   C)   D)   E)

A) <strong>Find the acceleration of a particle with the following position function.  </strong> A)   B)   C)   D)   E)
B) <strong>Find the acceleration of a particle with the following position function.  </strong> A)   B)   C)   D)   E)
C) <strong>Find the acceleration of a particle with the following position function.  </strong> A)   B)   C)   D)   E)
D) <strong>Find the acceleration of a particle with the following position function.  </strong> A)   B)   C)   D)   E)
E) <strong>Find the acceleration of a particle with the following position function.  </strong> A)   B)   C)   D)   E)
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6
Find the speed of a particle with the given position function. <strong>Find the speed of a particle with the given position function.  </strong> A)   B)   C)   D)   E)

A) <strong>Find the speed of a particle with the given position function.  </strong> A)   B)   C)   D)   E)
B) <strong>Find the speed of a particle with the given position function.  </strong> A)   B)   C)   D)   E)
C) <strong>Find the speed of a particle with the given position function.  </strong> A)   B)   C)   D)   E)
D) <strong>Find the speed of a particle with the given position function.  </strong> A)   B)   C)   D)   E)
E) <strong>Find the speed of a particle with the given position function.  </strong> A)   B)   C)   D)   E)
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7
Find the velocity of a particle that has the given acceleration and the given initial velocity.
<strong>Find the velocity of a particle that has the given acceleration and the given initial velocity.  </strong> A)   B)   C)   D)   E)

A) <strong>Find the velocity of a particle that has the given acceleration and the given initial velocity.  </strong> A)   B)   C)   D)   E)
B) <strong>Find the velocity of a particle that has the given acceleration and the given initial velocity.  </strong> A)   B)   C)   D)   E)
C) <strong>Find the velocity of a particle that has the given acceleration and the given initial velocity.  </strong> A)   B)   C)   D)   E)
D) <strong>Find the velocity of a particle that has the given acceleration and the given initial velocity.  </strong> A)   B)   C)   D)   E)
E) <strong>Find the velocity of a particle that has the given acceleration and the given initial velocity.  </strong> A)   B)   C)   D)   E)
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8
Find the acceleration of a particle with the given position function. <strong>Find the acceleration of a particle with the given position function.  </strong> A)   B)   C)   D)   E)

A) <strong>Find the acceleration of a particle with the given position function.  </strong> A)   B)   C)   D)   E)
B) <strong>Find the acceleration of a particle with the given position function.  </strong> A)   B)   C)   D)   E)
C) <strong>Find the acceleration of a particle with the given position function.  </strong> A)   B)   C)   D)   E)
D) <strong>Find the acceleration of a particle with the given position function.  </strong> A)   B)   C)   D)   E)
E) <strong>Find the acceleration of a particle with the given position function.  </strong> A)   B)   C)   D)   E)
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9
Find the velocity,acceleration,and speed of an object with position function Find the velocity,acceleration,and speed of an object with position function   for   Sketch the path of the object and its velocity and acceleration vectors. for Find the velocity,acceleration,and speed of an object with position function   for   Sketch the path of the object and its velocity and acceleration vectors. Sketch the path of the object and its velocity and acceleration vectors.
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10
The position function of a particle is given by
<strong>The position function of a particle is given by   When is the speed a minimum?</strong> A)   B)   C)   D)   E)
When is the speed a minimum?

A) <strong>The position function of a particle is given by   When is the speed a minimum?</strong> A)   B)   C)   D)   E)
B) <strong>The position function of a particle is given by   When is the speed a minimum?</strong> A)   B)   C)   D)   E)
C) <strong>The position function of a particle is given by   When is the speed a minimum?</strong> A)   B)   C)   D)   E)
D) <strong>The position function of a particle is given by   When is the speed a minimum?</strong> A)   B)   C)   D)   E)
E) <strong>The position function of a particle is given by   When is the speed a minimum?</strong> A)   B)   C)   D)   E)
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11
A projectile is fired from ground level with an initial speed of 1100 ft/sec and an angle of elevation of <strong>A projectile is fired from ground level with an initial speed of 1100 ft/sec and an angle of elevation of   </strong> A) Find the range of the projectile. B) What is the maximm height attained by the projectile? C) What is the speed of the projectile at impact? Round your answers to the nearest integer.

A) Find the range of the projectile.
B) What is the maximm height attained by the projectile?
C) What is the speed of the projectile at impact?
Round your answers to the nearest integer.
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12
A ball is thrown at an angle of <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)   to the ground.If the ball lands <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)   m away,what was the initial speed of the ball? Let <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)

A) <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)
B) <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)
C) <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)
D) <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)
E) <strong>A ball is thrown at an angle of   to the ground.If the ball lands   m away,what was the initial speed of the ball? Let  </strong> A)   B)   C)   D)   E)
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13
Find the scalar tangential and normal components of acceleration of a particle with position vector Find the scalar tangential and normal components of acceleration of a particle with position vector
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14
A force with magnitude <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   N acts directly upward from the xy-plane on an object with mass <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   kg.The object starts at the origin with initial velocity <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   Find its position function.

A) <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)   <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)
B) <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)
C) <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)
D) <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)
E) <strong>A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg.The object starts at the origin with initial velocity   Find its position function.</strong> A)       B)   C)   D)   E)
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