Question

A football player kicks a football in a field goal attempt. When the football reaches its maximum height, what is the relationship between the direction of the velocity and acceleration vectors? Assume air resistance is negligible.

A)A football player kicks a football in a field goal attempt. When the football reaches its maximum height, what is the relationship between the direction of the velocity and acceleration vectors? Assume air resistance is negligible.
B) At the maximum height, the velocity and acceleration vectors are parallel to each other.
C)At the maximum height, the velocity and acceleration vectors are perpendicular to each other.
D)At the maximum height, the velocity and acceleration vectors point in opposite directions.
E)At the maximum height, both the velocity and acceleration vectors are zero

Answer 1

Answer: C) At the maximum height, the velocity and acceleration vectors are perpendicular to each other.

Explanation: At the maximum height the ball stops going up and starts going down. Then, there is a given time at with the velocity of the ball (in the y-axis) is equal to zero.

And as you may know, every lifted object is pulled down by the gravitational force, thie means that the ball is accelerated when it is in the air, so the acceleration is not zero at the maximum height.

Here remember that the player kicked the ball in a given direction, so the ball has a compoent of velocity in the y-axis (that is zero at the point of maximum height) and a component in the x-axis.

Then, at maximum height the velocity is only in the x-direction, and the acceleration is pointing down (in the negative y-direction) so at this point the acceleration and the velocity are perpendiculars.

Answer 2

At position of maximum height we know that the vertical component of its velocity will become zero

so the object will have only horizontal component of velocity

so at that instant the motion of object is along x direction

while if we check the acceleration of object then it is due to gravity

so the acceleration of object is vertically downwards

so it is along y axis

so here these two physical quantities are perpendicular to each other

so correct answer would be

C)At the maximum height, the velocity and acceleration vectors are perpendicular to each other.