If an object is propelled upward from a height of s feet at an initial velocity of V feet per second, the. It’s height h after t seconds is given by equation

Question

H= -16t^+vt +s, where h is in feet if the object is propelled from a height of 12 feet with an initial velocity of 96 feet per secon, it’s height h is given by the equation h= -16t^+96t+12

after how many seconds is the height 120 feet

Answer 1

First, you need to fix the equation in the problem statement.  The correct equation is

 

h(t) = -16t² + vt + s

 

h(t) = -16t² + 96t + 12

 

Set h(t) = 120 and solve for t.

 

120 = -16t² + 96t + 12

 

-16t² + 96t - 108 = 0

 

Solve this quadratic equation for t, which you should know how to do.  You will get 2 positive solutions.  The lower t is the time it takes to reach 120 ft on the way up, and the higher t is the time it takes to reach 120 ft again on the way down.