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: 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.