Answer:
In order to catch the box before it hits the ground, the person needs to go as fast as approximately 5.96 m/s
Step-by-step explanation:
The height of the hot air balloon above the ground, s = 92.4 m
The location on the ground of the person intending to catch the box, x = 10 m away horizontally from the base location of the balloon
The time it takes the balloon released at zero vertical velocity is given by the following equation;
s = 1/2·g·t²
92.4 = 1/2 × 9.8 × t² = 19.6·t²
t² = 92.4/19.6 ≈ 4.714
t = √4.714 ≈ 1.68 seconds
The time, t, it takes the box to hit the ground ≈ 1.68 seconds
The speed, v, of the person standing 10 m away has to go to catch the box before it hits the ground is v = Distance/time =10/1.68 ≈ 5.96 m/s
In order to catch the box before it hits the ground, the person needs to go as fast as approximately 5.96 m/s.