Aprojectile trajectory has a maximum height h and a range r. the mass is m and the initial speed v0. the angle between the initial velocity and the horizontal direction is θ. acceleration of gravity is g. determine the magnitude of the angular momentum lo at the highest point with respect to o.

mvoh Cosθ

Explanation:

Velocity of projection = vo

Angle of projection = θ

acceleration due to gravity = g

Range = R

Maximum height = R

At highest point, the velocity has only horizontal component which always remains constant = vo Cosθ

At maximum height

linear momentum = mass x velocity = m vo Cos θ

Angular momentum = linear momentum x perpendicular distance

Lo = m x vo x Cos θ x h

Lo = mvoh Cosθ

Thus, the angular momentum about O is  mvoh Cosθ.