Aball 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

Answer

E. 14.2 seconds

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.

because it says use -2,0,and 2 for x, we can plug those numbers into the equation. y/4=3/4(-2)+2   y/4= -1 1/2 +2 now to get x by itself, we can multiply each side by 4. y=-6+8 which equals y=2 when x=-2. now you can do the same thing with 0 and 2 as x. you get y=8 when x=0 and y=14 when x=2.

x   |   y

-2 |   2

0   |   8

2   |   14

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