A projectile of mass 0.50 kg is fired with an initial speed of 10 m/s at an angle of 60° above the horizontal.The potential energy of the projectile-Earth system when the projectile is at its highest point (relative to the potential energy when the projectile is at ground level)is:
A)25 J
B)18.75 J
C)12.5 J
D)6.25 J
E)none of these

Question

Quizplus · Accepted Answer

At the highest point, the vertical component of the velocity is zero, and only the potential energy is considered. The initial kinetic energy can be used to find the maximum height using the equation $KE_i = PE_f$, where $KE_i = \frac{1}{2}mv^2_y$ and $PE_f = mgh$. The initial vertical velocity ($v_y$) can be found using $v_y = v\sin(\theta)$, where $v = 10 \, \text{m/s}$ and $\theta = 60^\circ$. Thus, $v_y = 10\sin(60^\circ) = 8.66 \, \text{m/s}$. The initial kinetic energy in the vertical direction is $KE_i = \frac{1}{2} \cdot 0.5 \cdot (8.66)^2 = 18.75 \, \text{J}$. This equals the potential energy at the highest point, so the correct answer is 18.75 J.

A Projectile of Mass 0