Answer
$P=92.2hp$
Work Step by Step
The required power can be determined as follows:
$Sigma F_y=ma_y$
$\implies 3(500)-1000=\frac{1000}{32.2}\times a$
$\implies a=1.6ft/s^2$
We know that
$v^2=v_{\circ}^2+2a(S-S_{\circ})$
$\implies v^2=(0)^2+(2\times 16(15-0))=21.98ft/s$
The power output is given as
$P_o=Fv=3\times 500\times 21.98=32970lb\cdot ft/s$
The efficiency of the motor is
$\epsilon=\frac{P_o}{P_i}$
$\implies 0.65=\frac{32970}{P_i}$
$\implies P_i=50723lb\cdot ft/s=\frac{50723}{500}hp=92.2hp$
