A ball is thrown vertically in the air with a velocity of 100ft/s. Use the projectile formula h=−16t2+v0t to determine at what time(s), in seconds, the ball is at a height of 150ft.

Question

A ball is thrown vertically in the air with a velocity of 100ft/s. Use the projectile formula h=−16t2+v0t to determine at what time(s), in seconds, the ball is at a height of 150ft. Round your answer(s) to the nearest tenth of a second.

Answer 1

the height function is h = -16t^2 + 100t

150 = -16t^2 + 100t

0 = -16t^2 + 100t - 150

0 = -8t^2 + 50t - 75

0 = 8t^2 - 50t + 75

t = [50 +or- sqrt( 2500 - 4*8*75)] / 16

= [ 50 +or- sqrt( 2500 - 2400)]/ 16

= [ 50 +or- sqrt(100) ] / 16

= [ 50 +or- 10 ]/ 16

t = 60/16 = 30/8 = 15/4

or

t = 40/16 = 20/8 = 10/5 = 5/2