Find time it takes projectile to land with function

Question

Step 1.) The height h of a projectile launched from ground level is a function of the time t it is in the air. The height in feet for t seconds is given by the function h(t) = −16t² + 48t. What is the domain?

I've deduced the domain is [0,3]

Step 2.) After the projectile is launched from ground level it takes _____  seconds for the projectile to return to the ground.

Step 2 would like me to fill in the blank with an exact number. How am I supposed to find an exact number with the domain [0,3] ? Wouldn't a domain suggest variable outputs?

Answer 1

I'm unsure how you deduced the domain is [0, 3] without solving the problem but the graph of the height vs the time is an inverted parabola. Remember the domain is the possible values of the independent variable (which in this case is "t"). If we let t = 0 and plug it into the equation we get:

h(t) = -16t² + 48t

h(0) = -16(0)² + 48(0) = 0

So at time t = 0, the height is 0 feet (which makes perfect sense).

At time t = 3, the height is:

h(3) = -16(3)² + 48(3) = 0

So we see that at time t = 3, the height is again 0 feet.

Let's try at t = 1.5 (halfway between t = 0 and t = 3):

h(1.5) = -16(1.5)² + 48(1.5) = 36

So we see that at time t = 3, the height is 36 feet.

Are you getting the picture?

If the projectile was at zero, then went to 36 feet and the came back to zero, then the time it was in the air was 3 seconds. They are asking how many seconds go by until the height gets back to zero.