The height of an object tossed upward with an initial velocity of 120 feet per second is given by the formula h = −16t2 + 120t, where h is the height in feet and t is the time in seconds,

Question

The height of an object tossed upward with an initial velocity of 120 feet per second is given by the formula h = −16t2 + 120t, where h is the height in feet and t is the time in seconds. Find the time required for the object to return to its point of departure.

Answer 1

h=-16t^2+120t

this is a quadratic equation

-16t^2+120t-h=0

or 16t^2-120t+h=0 so

h=0 both at take off and landing

16t^2-120t=0

8t(2t-15)=0

t=0 or t=7.5

so 7.5 seconds is the time

Answer 2

Hi Munira,

At point of departure, the height (h) is 0, so:

h=0

We need to solve for t:

0 = -16t² +120t

Now, we can factor out a -8t:

-8t(2t -15) = 0

So, we now have:

-8t = 0 or

2t - 15 = 0

t = 0

or

2t -15 = 0

2t = 15

t = 7.5

Now, we know t is 0 when the object first launches, so we have to go with:

t = 7.5 seconds, the time it takes to return to point of launch

I hope this helps.