When will the height be 443 feet? When will the object reach the ground?

Question

An object is thrown upward at a speed of 181 feet per second by a machine from a height of 8 feet off the ground. The height h of the object after t seconds can be found using the equation h=−16t^2+181t+8



When will the height be 443 feet?

When will the object reach the ground? 

Answer 1

Plug in 443 feet for h to find the time where the object reach that high.

-16t² + 181t + 8 = 443

-16t² + 181t - 435 = 0

Use the quadratic formula to find t. Let a = -16, b = 181, and c = -435.

t = -b ± √(b² - 4ac) / 2a = -181 ± √[181² - 4(-16)(-435)] / 2(-16) = -181 ± √(4921) / (-32) = {3.464 , 7.848}

Plug in 0 feet for h to see when the object reach the ground.

-16t² + 181t + 8 = 0

Use the quadratic formula to find t when h = 0. Let a = -16, b = 181, and c = 8.

t = -b ± √(b² - 4ac) / 2a = -181 ± √[181² - 4(-16)(8)] / 2(-16) = -181 ± √(33273) / (-32) = {-0.044 , 11.357}

The object will reach the height of 443 feet at 3.464 seconds and then at 7.848 seconds. The object will reach the ground at 11.357 seconds.