Question

If an object is projected upward with an initial velocity of 48 ft per second from a height h of 64 ft, then its height t seconds after it is projected is defined by the equation f(t) = -16(t) with superscript (2) + 48t + 64. How many seconds after it is projected will it hit the ground?

Answer 1

4 seconds

Explanation:

Given that :

Height of a projected object is modeled by:

f(t) = - 16t² + 48t + 64

t = height

How many seconds after projection will it hit the ground ;

When the projectile hits the ground ; t = 0

f(t) = - 16t² + 48t + 64

f(t) = 0

- 16t² + 48t + 64 = 0

Divide through by - 16

t² - 3t - 4 = 0

t² - 4t + t - 4 =0

t(t - 4) +1(t - 4) = 0

(t +1) = 0 or (t - 4) = 0

t = - 1 or t = 4

t can't be negative ;

Hence, the projectile will hit the ground after 4 seconds