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.

Solution

Note: At the angle of projection, the initial velocity has two components, v_x = v_icosθ and v_y = v_isinθ . 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.