math problem

Question

A projectile is fired straight up from a 20ft building with an initial velocity of 100 ft/sec. The equation h=-16t^2+100t+20 models the projectile's height in seconds. In how many seconds will the projectile reach the ground?

Answer 1

The projectile reaches the ground when h(t) = 0.

 

-16t^2 + 100t + 20 = 0

 

Find t from the quadratic formula:

 

t = 1/[2(-16)] {-100 ± √[(100)^2 - 4(-16)(20)]}

 

t = 1/[2(-16)] [-100 ± √(10000 + 1280)]

 

t = 1/[2(-16)] (-100 ± 106.21) = (-1/32)(-100 ± 106.21)

 

t > 0, and only the negative square root makes t > 0, so

 

t = (-1/32)(-100 - 106.21) = 6.44 seconds