Question

In case of a projectile motion, what is the angle between the velocity and acceleration at the highest point?
A. $0^\circ $
B. $45^\circ $
C. $90^\circ $
D. $180^\circ $

Answer 1

Hint: First we need to draw a rough diagram representing all the required parameters to solve the given problem. The main parameters in this problem are the velocity and the acceleration. Now with the help of a diagram and using the projectile motion concept we can find the correct option given in the above problem.

Complete step by step answer:
As per the problem we have to find the angle between the velocity and acceleration at the highest point. Now when a particle is projected an angle of $\theta $, having some initial velocity u moving along a curved path under constant acceleration acting in downward direction can be represented as given,

As per the diagram H is the highest point of the projectile motion and at the highest point the velocity acting is $u\cos \theta $ and the acceleration acting on the particle is the constant acceleration and it is acting in downward direction and it the acceleration due to gravity. Hence acceleration and velocity are perpendicular to each other. Now from the above figure and from the above discussion we can conclude that the angle between the velocity and acceleration at the highest point is $90^\circ $.

Therefore, the correct answer is option C.

Note: Remember here the projectile motion is defined as when a particle is through obliquely from the earth’s surface and will move in a curved path under the action of constant acceleration and that is directed towards the center of the earth. Keep in mind that here the particle is assumed to remain close to the surface of the earth.