193k views
0 votes
A ball is released from a hot air balloon moving downward with a velocity of -10.0 meters/second and a height of 1,000 meters. How long did it take the ball to reach the surface of Earth? Given: g = -9.8 meters/second2. A. 11.2 seconds B. 12.1 seconds C. 13.3 seconds D. 13.5 seconds E. 14.2 seconds

1 Answer

3 votes

Answer

E. 14.2 seconds


Step-by-step explanation

We are going to use the Newton's law of motion.

s = ut + (1/2)gt²

Where s ⇒ height

g ⇒ acceleration due to gravity

t ⇒ time taken to reach the surface of the earth.

u ⇒ initial velocity

s = ut + (1/2)gt²

1,000 = -10t + (1/2)×-9.8×t²

10t + (1/2)×9.8×t² = -1000

4.9t² + 10t = -1000

t² + 2.0408t = 204.0816

t² + 2.0408t + 1.0204² = 204.0816 + 1.0204²

(t + 1.0204)² = 205.1228

t = +√205.1228 -1.0204 or t = -√205.1228 -1.0204

= 14.322 s = - 15.342 s

Since time can not be negative, we take the answer to be: 14.322 seconds.

User Atalantus
by
7.9k points