The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = -16t2 + 96t, where t is the time in seconds.

Question

The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = −16t2 + 96t, where t is the time in seconds.

a) How long will it take the object to reach a height of 144 feet?

b) How long will it take the object to return to the point of departure?

Answer 1

All right. You have this quadratic equation:

 

16 t^2 - 96 t + h = 0

 

The solution to this is always

 

t = (96 +/- [96^2 - 64h]^(1/2)) / 64

 

and if h =144 ft, then t = 1.5 s. You can verify that, right?

 

If you want to get back to the point of departure, that's - I'm gonna say - h=0. So for that, t=0 (starting point) or t = 3 s.

 

Sanity check: if the 144 ft height in the first problem is actually the midpoint of flight, everything will make sense. That's what you look for.

 

Cheers!