Question

A small sphere of mass m is launched horizontally over a body of water from a height h above the water and with a launch speed v₀. Determine expressions for the following in terms of m, v₀, h, and g. Air resistance is negligibly small.

(a) W is the amount work done by the force of gravity on the projectile during its flight.

W =

(b) ΔKE is the change in kinetic energy ΔKE of the projectile from the time it was fired until it hits the water.

ΔKE =

(c) KE_f is the final kinetic energy KE_f of the projectile as it hits the water.

KEf =

(d) Are any of the answers changed if the initial angle is changed?

Answer 1

a)

$W=9.81h$

b)

$t^{2}=\frac{2h}{g}$

$v_{y}=-gt=-\sqrt{2gh}$

$v_{x}=v_{0}$

Final velocity (magnitude)

$v_{f}=\sqrt{2gh+v_{0}^{2}}$

Change in Kinetic energy:

$\Delta KE=\frac{1}{2}m(v_{0}^{2}-2gh-v_{0}^{2})$

$\Delta KE=-\frac{1}{2}m(2gh)$

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Final Kinetic energy:

$KEf=\frac{1}{2}m(2gh+v_{0}^{2})$