Quadratic function

Question

a ball is thrown upward from the top of a 160-foot-high building. The ball is 192 feel above ground level after 1 second, and it reaches ground level in 5 seconds. The height above ground is a quadratic function of the time after the ball is thrown. Write the equation of this function.

Answer 1

h(t) = -(1/2)gt² + vt + h₀

 

g = 32 ft/s²

v = ?

h₀ = 160 ft

 

h(t) = -16t² + vt + 160

 

h(1) = 192 ft ⇒

 

192 = -16(1)² + v(1) + 160

 

v = (192 + 16 - 160) ft/s = 48 ft/s

 

h(t) = -16t² + 48t + 160

 

Test the answer: 

 

Is h(5) = 0 ?