Question 1

Suppose that several projectiles are fired upward. Which one will be in the air longest? (R is range, h is highest elevation, and t is time of flight.)
A) The one with the highest maximum elevation, h
B) The one with the greatest initial velocity
C) The one with the minimum elevation, h
D) The one with the farthest range, R
E) The one for which the product of (R)(t)(h) is maximum

Accepted Answer

The time a projectile is in the air is most directly influenced by its maximum elevation, h. The higher the projectile goes, the longer it will stay in the air due to the longer ascent and descent times, regardless of its range or initial velocity.

Question 2

You are serving the volleyball for the second time in a volleyball game. If the ball leaves your hand with twice the velocity it had on your first serve, its horizontal range R (compared to your first serve) would be
A)  times as much.
B) twice as much.
C) 2  times as much.
D) four times as much.
E) half as much.

Accepted Answer

The answer of You are serving the volleyball for the...

Question 3

At what angle should a water-gun be aimed in order for the water to land with the greatest horizontal range?
A) 30°
B) 0°
C)  $\pi$ radians
D) 90°
E) 45°

Accepted Answer

The greatest horizontal range for a projectile under the influence of gravity (assuming no air resistance) is achieved at a launch angle of 45°.

Question 4

The acceleration of gravity on the moon is only one-sixth of that on Earth. If you hit a baseball on the moon with the same effort (and at the speed and angle) that you would on Earth, the ball would travel
A) one-sixth as far.
B)  as far.
C) the same distance away.
D) 6 times as far.
E) 36 times as far.

Accepted Answer

The answer of The acceleration of gravity on the moon...

Question 5

You throw a pebble upward as shown, with a velocity v_o at an angle ?, from a roof (at point J) Figure 3-6 If the pebble rises upward to h ft above the roof (to point K), then falls to the ground below (to point L), its speed when it hits the ground is A) between vo and 2v_o B) greater than 2 v_o C) v_o D) 2 v_o E) v_o

Accepted Answer

The answer of You throw a pebble upward as shown,...

Question 6

Consider throwing a shotput at a 45.° elevation. The ratio of range to height (R/h) would be A) 2 B) 2² C) 2⁴ D) E) 2

Accepted Answer

The answer of Consider throwing a shotput at a 45.°...

Question 7

If you want to cross a river in a motorboat in the least amount of time (least time in water), you should head
A) the time will be independent of how you head your boat
B) slightly downstream.
C) directly downstream.
D) slightly upstream.
E) straight across the river.

Accepted Answer

To cross a river in the least amount of time, you should aim the motorboat straight across the river. This minimizes the distance traveled over water, directly opposing the river's current, and thus takes the least amount of time. Heading in any other direction would result in a longer path due to the river's current affecting the boat's trajectory.

Question 8

Consider a plane flying with groundspeed V_g and airspeed V_a in a wind with velocity V. Which of the following relationships is true? A) V_g can be greater than V_a + V B) V_g = V_a - V C) V_g = V_a + V D) V_g can be less than V_a + V E) V_g can have any value between V_a + V and V_a - V

Accepted Answer

The groundspeed of a plane (V_g) is the vector sum of its airspeed (V_a) and the wind velocity (V). Depending on the direction of the wind relative to the plane's heading, the groundspeed can be greater than the airspeed plus the wind speed, less than the airspeed plus the wind speed, or somewhere in between. Therefore, the groundspeed can vary within a range defined by adding or subtracting the wind velocity from the airspeed.

Question 9

Consider a velocity with components 36. m/s Westward and 22. m/s Northward. What is its magnitude and direction?

Accepted Answer

The answer of Consider a velocity with components 36. m/s...

Question 10

A particle initially moving with a velocity 2 m/s experiences a constant acceleration of 1 m/s² in the +x-direction and -2 m/s² in the y-direction. What are the velocity components of the particle after 4 s?

Accepted Answer

The answer of A particle initially moving with a velocity...

Question 11

Two vectors A and B have components (0, 1, 2) and (-1, 3, 1), respectively. 
(a) Determine the components of the sum of these two vectors. 
(b) Determine the magnitude of the sum of these two vectors.

Accepted Answer

The answer of Two vectors A and B have components...

Question 12

-For the three vectors given in Figure 3-7, determine the vector "difference" - - .

Accepted Answer

The answer of 
-For the three vectors given in Figure...

Question 13

-Given the three vectors in Figure 3-7, determine the vector sum + + .

Accepted Answer

The answer of 
-Given the three vectors in Figure 3-7,...

Question 14

-For the three vectors shown in Figure 3-7, determine +- .

Accepted Answer

The answer of 
-For the three vectors shown in Figure...

Question 15

The magnitude of a vector is 3.1 units and its x component is 0 units. What are the possible y components and respective angles with the x-axis of the vector?

Accepted Answer

The answer of The magnitude of a vector is 3.1...

Question 16

Lisa throws a stone horizontally from the roof edge of a 50. meter high dormitory. It hits the ground at a point 60. m from the building. Find the time of flight.

Accepted Answer

The answer of Lisa throws a stone horizontally from the...

Question 17

A marble rolls off the edge of a table top with a speed of 2.0 m/s. What is the magnitude of its velocity 0.10 s later?

Accepted Answer

The answer of A marble rolls off the edge of...

Question 18

A mortar shell is launched with a velocity of 100 m/s at an angle of 30.0° above horizontal from a point on a cliff 50.0 m above a level plain below. How far from the base of the cliff does the mortar shell strike the ground?

Accepted Answer

The answer of A mortar shell is launched with a...

Question 19

A rifle bullet is fired at an angle of 30° below the horizontal with an initial velocity of 800 m/s from the top of a cliff 80 m high. How far from the base of the cliff does it strike the level ground below?

Accepted Answer

The answer of A rifle bullet is fired at an...

Question 20

Suppose David Ortiz hits a home run which travels 361. feet (110. m). Assuming it left the bat at 50.°, how fast was it hit?

Accepted Answer

The answer of Suppose David Ortiz hits a home run...

Quiz 3: Motion in Two Dimensions

Suppose that several projectiles are fired upward. Which one will be in the air longest? (R is range, h is highest elevation, and t is time of flight.)

You are serving the volleyball for the second time in a volleyball game. If the ball leaves your hand with twice the velocity it had on your first serve, its horizontal range R (compared to your first serve) would be

At what angle should a water-gun be aimed in order for the water to land with the greatest horizontal range?

The acceleration of gravity on the moon is only one-sixth of that on Earth. If you hit a baseball on the moon with the same effort (and at the speed and angle) that you would on Earth, the ball would travel

You throw a pebble upward as shown, with a velocity v_o at an angle ?, from a roof (at point J) Figure 3-6 If the pebble rises upward to h ft above the roof (to point K) , then falls to the ground below (to point L) , its speed when it hits the ground is

Consider throwing a shotput at a 45.° elevation. The ratio of range to height (R/h) would be

If you want to cross a river in a motorboat in the least amount of time (least time in water) , you should head

Consider a plane flying with groundspeed V_g and airspeed V_a in a wind with velocity V. Which of the following relationships is true?

Consider a velocity with components 36. m/s Westward and 22. m/s Northward. What is its magnitude and direction?

A particle initially moving with a velocity 2 m/s experiences a constant acceleration of 1 m/s² in the +x-direction and -2 m/s² in the y-direction. What are the velocity components of the particle after 4 s?

Two vectors A and B have components (0, 1, 2) and (-1, 3, 1), respectively. (a) Determine the components of the sum of these two vectors. (b) Determine the magnitude of the sum of these two vectors.

-For the three vectors given in Figure 3-7, determine the vector "difference" - - .

-Given the three vectors in Figure 3-7, determine the vector sum + + .

-For the three vectors shown in Figure 3-7, determine +- .

The magnitude of a vector is 3.1 units and its x component is 0 units. What are the possible y components and respective angles with the x-axis of the vector?

Lisa throws a stone horizontally from the roof edge of a 50. meter high dormitory. It hits the ground at a point 60. m from the building. Find the time of flight.

A marble rolls off the edge of a table top with a speed of 2.0 m/s. What is the magnitude of its velocity 0.10 s later?

A mortar shell is launched with a velocity of 100 m/s at an angle of 30.0° above horizontal from a point on a cliff 50.0 m above a level plain below. How far from the base of the cliff does the mortar shell strike the ground?

A rifle bullet is fired at an angle of 30° below the horizontal with an initial velocity of 800 m/s from the top of a cliff 80 m high. How far from the base of the cliff does it strike the level ground below?

Suppose David Ortiz hits a home run which travels 361. feet (110. m). Assuming it left the bat at 50.°, how fast was it hit?

Quiz 3: Motion in Two Dimensions

Suppose that several projectiles are fired upward. Which one will be in the air longest? (R is range, h is highest elevation, and t is time of flight.)

You are serving the volleyball for the second time in a volleyball game. If the ball leaves your hand with twice the velocity it had on your first serve, its horizontal range R (compared to your first serve) would be

At what angle should a water-gun be aimed in order for the water to land with the greatest horizontal range?

The acceleration of gravity on the moon is only one-sixth of that on Earth. If you hit a baseball on the moon with the same effort (and at the speed and angle) that you would on Earth, the ball would travel

You throw a pebble upward as shown, with a velocity vo at an angle ?, from a roof (at point J) Figure 3-6 If the pebble rises upward to h ft above the roof (to point K) , then falls to the ground below (to point L) , its speed when it hits the ground is

Consider throwing a shotput at a 45.° elevation. The ratio of range to height (R/h) would be

If you want to cross a river in a motorboat in the least amount of time (least time in water) , you should head

Consider a plane flying with groundspeed Vg and airspeed Va in a wind with velocity V. Which of the following relationships is true?

Consider a velocity with components 36. m/s Westward and 22. m/s Northward. What is its magnitude and direction?

A particle initially moving with a velocity 2 m/s experiences a constant acceleration of 1 m/s2 in the +x-direction and -2 m/s2 in the y-direction. What are the velocity components of the particle after 4 s?

Two vectors A and B have components (0, 1, 2) and (-1, 3, 1), respectively. (a) Determine the components of the sum of these two vectors. (b) Determine the magnitude of the sum of these two vectors.

-For the three vectors given in Figure 3-7, determine the vector "difference" - - .

-Given the three vectors in Figure 3-7, determine the vector sum + + .

-For the three vectors shown in Figure 3-7, determine +- .

The magnitude of a vector is 3.1 units and its x component is 0 units. What are the possible y components and respective angles with the x-axis of the vector?

Lisa throws a stone horizontally from the roof edge of a 50. meter high dormitory. It hits the ground at a point 60. m from the building. Find the time of flight.

A marble rolls off the edge of a table top with a speed of 2.0 m/s. What is the magnitude of its velocity 0.10 s later?

A mortar shell is launched with a velocity of 100 m/s at an angle of 30.0° above horizontal from a point on a cliff 50.0 m above a level plain below. How far from the base of the cliff does the mortar shell strike the ground?

A rifle bullet is fired at an angle of 30° below the horizontal with an initial velocity of 800 m/s from the top of a cliff 80 m high. How far from the base of the cliff does it strike the level ground below?

Suppose David Ortiz hits a home run which travels 361. feet (110. m). Assuming it left the bat at 50.°, how fast was it hit?

You throw a pebble upward as shown, with a velocity v_o at an angle ?, from a roof (at point J) Figure 3-6 If the pebble rises upward to h ft above the roof (to point K) , then falls to the ground below (to point L) , its speed when it hits the ground is

Consider a plane flying with groundspeed V_g and airspeed V_a in a wind with velocity V. Which of the following relationships is true?

A particle initially moving with a velocity 2 m/s experiences a constant acceleration of 1 m/s² in the +x-direction and -2 m/s² in the y-direction. What are the velocity components of the particle after 4 s?