How many seconds?

Question

If an object is propelled upward from a height of 48 feet at an initial velocity of 64 feet per second, then its height after t seconds is given by the equation h(t)= -16t^2+64t+48, where height is in feet. After how many seonds will the object reach a height of 112 feet? 

Answer 1

You are given height as a function of time:

 

h(t) = -16t² + 64t + 48

 

with h in feet, t in seconds.  You want to find t so that h(t) = 112 ft.  Then

 

112 = -16t² + 64t + 48

 

-16t² + 64t - 64 = 0

 

Simplify a bit to get

 

t² - 4t + 4 = 0 = (t - 2)²

 

It reaches 112 ft in 2 seconds.  Note the perfect square also tells you that 112 feet is its maximum height.  If you did not get a perfect square, you would have 2 times.  The lower time would be the time to reach 112 ft on the way up and the higher time would be the time to reach 112 ft on the way down.