Problem 10: Calculate the angle of projection for which K.E at the highest point of its trajectory is equal to one fourth of its K.E at the point of projection.
Note: At the angle of projection, the initial velocity has two components, vx = vicosθ and vy = visinθ . At the highest point, the y-component of the velocity becomes 0 and the x-component undergoes no change.
Given: K.E at the point of projection = 4× K.E at the highest point
Now K.E at the point of projection
And K.E at the highest point
Now according to the condition of the question,
Therefore, angle of projection is 600.