Question 10: Calculate the angle of projection for which K.E at summit of its trajectory is equal to one-fourth of its K.E at point of projection.
Projectile is a two-dimensional motion. The projectile has a horizontal velocity vx and vertical velocity vy. If vi is the resultant initial velocity, then by Pythagoras theorem
The initial K.E will be,
At the summit point, the vertical part is zero and horizontal is the same. Therefore, at summit
The K.E at the summit point will be,
The condition of the problem is K.E at the summit is one-fourth of the K.E at the initial point. Therefore, from equations (A) and (B), we have,
Thus if θ=60°, the K.E of the projectile at the summit would be one-fourth of the K.E at the point of projection.