Answer
(a) Superman's minimum constant acceleration should be $294~m/s^2$
(b) Superman's speed will be 266 m/s
Work Step by Step
(a) We can find the time it takes for the rock to fall 4.0 m:
$\Delta y = \frac{1}{2}a_yt^2$
$t = \sqrt{\frac{2\Delta y}{a_y}}$
$t = \sqrt{\frac{(2)(4.0~m)}{9.80~m/s^2}}$
$t = 0.904~s$
We can find Superman's minimum constant acceleration:
$\Delta x = \frac{1}{2}a_xt^2$
$a_x = \frac{2\Delta x}{t^2}$
$a_x = \frac{(2)(120~m)}{(0.904~s)^2}$
$a_x = 294~m/s^2$
Superman's minimum constant acceleration should be $294~m/s^2$
(b) We can find Superman's velocity when he reaches Lois Lane:
$v_f^2 = v_0^2+2a_x\Delta x$
$v_f = \sqrt{v_0^2+2a_x\Delta x}$
$v_f = \sqrt{0+(2)(294~m/s^2)(120~m)}$
$v_f = 266~m/s$
Superman's speed will be 266 m/s
