# College Physics with Mastering Physics

Physics & Astronomy

## Quiz 3 :Motion in Two Dimensions

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The x -component of a velocity vector that has an angle of 37° to the + x -axis has a magnitude of 4.8 m/s. (a) What is the magnitude of the velocity (b) What is the magnitude of the y -component of the velocity
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(a)
The vector
makes an angle
with the positive
-axis
The
-component of vector
is
However, we know that the formula for the horizontal component of the vector is
Now,
, then
The magnitude of the velocity vector is
(b) The magnitude of the
-component of the velocity is

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Which one of the following cannot be a true statement about an object: (a) It has zero velocity and a nonzero acceleration; (b) it has velocity in the x -direction and acceleration in the y -direction; (c) it has velocity in the y -direction and acceleration in the y -direction; of (d) it has constant velocity and changing acceleration
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The false statement is (d) it has constant velocity and changing acceleration.
Acceleration, whether it's changing or constant, always changes the velocity either by changing direction or the magnitude.

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For an object in curvilinear motion, (a) the object's velocity components are constant, (b) the y -velocity component is necessarily greater than the x -velocity component, there is an acceleration nonparallel to the object's path the velocity and acceleration vectors must be at right angles (90°).
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A particle is said to execute curvilinear motion when it moves in a curved path.
A particle in curvilinear motion has constant horizontal component of velocity. But the vertical velocity component change. Though the magnitude of the velocity remains constant, the direction of the velocity changes. Hence the components of velocity are not equal.
Therefore option (a) is incorrect.
The horizontal and vertical components of velocity are equal only when the angle of projection is
. If the angle of projection is less than that, the horizontal component is greater than the vertical component.
Therefore option (b) is incorrect.
The acceleration and velocity are perpendicular only at the maximum height. At all other points, they are not perpendicular.
Therefore option (d) is incorrect.
The horizontal component of the velocity of the projected object is constant, so the horizontal component of acceleration is zero. The vertical component of the projected object decreases as increase in its height. So, the object has only vertical component of acceleration that is acceleration due to gravity. The acceleration due to gravity has direction along vertical. The direction of velocity of the projectile always changes its direction and magnitude. So, in this situation, the direction of the velocity is non-parallel to the acceleration.
Therefore option (c) is correct.

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(a) Can a vector be less than one of its components (b) How about equal to one of its components
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A golf ball is hit with an initial speed of 35 m/s at an angle less than 45° above the horizontal. (a) The horizontal velocity component is (1) greater than, (2) equal to, (3) less than the vertical velocity component. Why (b) If the ball is hit at an angle of 37°, what are the initial horizontal and vertical velocity components
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If the magnitude of a velocity vector is 7.0 m/s and the x -component is 3.0 m/s, what is the y -component
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Can the x -component of a vector be greater than the magnitude of the vector How about the y -component Explain.
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A student strolls diagonally across a level rectangular campus plaza, covering the 50-m distance in 1.0 min (Fig.). (a) If the diagonal route makes a 37° angle with the long side of the plaza, what would be the distance travelled if the student had walked halfway around the outside of the plaza instead of along the diagonal route (b) If the student had walked the outside route in 1.0 min at a constant speed, how much time would she have spent on each side FIGURE Which way See Exercise.
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Is it possible for an object's velocity to be perpendicular to the object's acceleration If so, describe the motion.
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On Cartesian axes, the x -component of a vector is generally associated with a (a) cosine, (b) sine, (c) tangent, (d)none of the foregoing.
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What are the conditions for two vectors to add to zero
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The x - and y -components of an acceleration vector are 3.0 m/s 2 and 4.0 m/s 2 , respectively. (a) The magnitude of the acceleration vector is (1) less than 3.0 m/s 2 , (2) between 3.0 m/s 2 and 4.0 m/s 2 , (3) between 4.0 m/s 2 and 7.0 m/s 2 , (4) equal to 7.0 m/s 2. (b) What are the magnitude and direction of the acceleration vector
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Can a nonzero vector have a zero x -component Explain.
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An airplane climbs at an angle of 15° with a horizontal component of speed of 200 km/h. (a) What is the plane's actual speed (b) What is the magnitude of the vertical component of its velocity
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The equation applies (a) to all kinematic problems, (b) only if is zero, (c) to cons accelerations, (d) to negative times.
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Two linear vectors of magnitudes 3 and 4 are added. The magnitude of the resultant vector is (a) 1, (b) 7, between 1 and 7.
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Describe the motion of an object that is initially traveling with a constant velocity and then receives an acceleration of constant magnitude (a) in a direction parallel to the initial velocity, (b) in a direction perpendicular to the initial velocity, and (c) that is always perpendicular to the instantaneous velocity or direction of motion.
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Is it possible to add a vector quantity to a scalar quantity
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