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.

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.  

180 square centimeters

step-by-step explanation: