Answer:
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.
