Question

A ball is thrown downward with an initial velocity of 35 meters per second from a

cliff that is 120 meters high. The height of the ball is given by the quadratic

equation h = - 4.9t2 - 35t +120 where h is in meters and t is the time in seconds

since the ball was thrown. Find the time it takes the ball to hit the ground. Round

your answer to the nearest tenth of a second.

Answer 1

Answer: 2.5 seconds.

Step-by-step explanation:

Hi, since when the ball hits the ground the height = 0, to answer this question we have to substitute h=o in the equation:  

h = - 4.9t2 - 35t +120

0 = - 4.9t2 - 35t +120

Applying the quadratic formula:

For: ax2+ bx + c  

x =[ -b ± √b²-4ac] /2a  

Replacing with the values given:  

x =[ -(-35) ± √(-35)²-4(-4.9)120] /2(-4.9)  

x = [ 35 ± √1,225 +2,352] /-9.8

x = [ 35 ± √3,577] /-9.8

x = [ 35 ±59.8 ] /-9.8

Positive:  

x = [ 35 + 59.8] /-9.8 = 94.8 /-9.8 = -9.67 seconds

Negative:  

x = [ 35 - 59.8] /-9.8 = -24.8 /-9.8 = 2.5 seconds

Since the time can't be negative, the answer is 2.5 seconds.

Feel free to ask for more if needed or if you did not understand something.