Answer
For the dart to hit the monkey before the monkey reaches the ground, the minimum muzzle velocity of the dart is 31 m/s.
Work Step by Step
We can find the time for the monkey to fall 25 meters.
$y = \frac{1}{2}gt^2$
$t = \sqrt{\frac{2y}{g}} = \sqrt{\frac{(2)(25~m)}{9.80~m/s^2}}$
$t = 2.259~s$
Let $v$ be the muzzle velocity of the dart.
$v = \frac{x}{t} = \frac{70~m}{2.259~s} = 31~m/s$
For the dart to hit the monkey before the monkey reaches the ground, the minimum muzzle velocity of the dart is 31 m/s
