An object of mass m is projected from the origin in a vertical plane at 45° to the horizontal with initial speed v₀. The magnitude and direction of the angular momentum about the origin when it reaches the highest point is

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(4) (mv₀³)/(4√2 g) along -z. At the top, speed is horizontal vₓ=v₀ cos 45°=(v₀)/(√2) at height H=(v₀² sin² 45°)/(2g)=(v₀²)/(4g). L=m vₓ H=m(v₀)/(√2)(v₀²)/(4g)=(mv₀³)/(4√2 g), directed into the page (-z) for motion in the +x, +y plane.

An object of mass m is projected from the origin in a vertical plane at 45° to the horizontal with initial speed v₀. The magnitude and direction of the angular momentum about the origin when it reaches the highest point is

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