Question

A particle (mass m) is projected with an initial velocity $v$ at an angle $\theta$ to the horizontal. What is the work done by the force of gravity from the instant of throwing to the instant it reaches the highest point?

• A. $mv^{2} \sin \theta$
• B. Zero
• C. $-mv^{2} \sin \theta$
• D. $\frac{mv^{2} \sin^{2} \theta}{2}$

Answer 1

Answer: (D)

$W_{m g} =K_{f}-K_{i}$
$=\frac{1}{2} m(v \cos \theta)^{2}-\frac{1}{2} m v^{2}$
$=\frac{1}{2} m v^{2}\left[\cos ^{2} \theta-1\right]$
$=-\frac{1}{2} m v^{2} \sin ^{2} \theta$