A rock is thrown down with a velocity of 20 feet per second from a hot air balloon that is 220 feet above the ground. How long will it take for the rock to reach the ground?​

It takes the rock approximately 4.96 seconds to reach the ground

Step-by-step explanation:

The given parameters of the rock thrown down from the hot air balloon are;

The (initial) downward velocity with which the rock was thrown down, u = 20 feet/second

The height of the balloon when the rock was thrown down, h = 220 feet

According to the kinetic equation of motion, we have;

h = u·t + (1/2)·g·t²

Where;

h = The height of the rock when it was thrown = 220 ft.

u = The initial velocity of the rock = 20 ft./s

g = The acceleration due to gravity acting on the rock = 9.81 m/s²

t = How long it takes the rock to reach the ground

Plugging in the values gives;

220 = 20·t + (1/2)×9.81×t²

4.905·t² + 20·t - 220 = 0

Therefore;

t = (-20 ± √(20² - 4×4.905×(-220)))/(2 × 4.905)

t ≈ 4.96, or t ≈ -9.04

Therefore, the time it takes the rock to reach the ground, t ≈ 4.96 seconds.