A ship fires a cannonball toward the sea. The height, in feet, of the cannonball above the water, h, is a function of the number of seconds the cannonball has been in the air, t.

Question

h(t)=-16t^2+60t+16
Which expression shows the height of the cannonball in a way that tells when the cannonball will strike the surface of the water?

Answer 1

To determine when the cannonball will strike the surface of the water, we need to find when the height of the cannonball, h(t), is equal to 0.

So, we set h(t) equal to 0:

0 = -16t^2 + 60t + 16

This equation can be rearranged as:

16t^2 - 60t - 16 = 0

Now, to find the time when the cannonball will strike the surface, we can use the quadratic formula:

t = (-(-60) ± √((-60)^2 - 4*16*(-16))) / (2*16)

t = (60 ± √(3600 + 1024)) / 32

t = (60 ± √4624) / 32

t = (60 ± 68) / 32

This gives two possible solutions:

t = (60 + 68) / 32 = 128 / 32 = 4 seconds

t = (60 - 68) / 32 = -8 / 32 = -0.25 seconds

The positive value, 4 seconds, represents the time it will take for the cannonball to strike the water. Thus, the expression that shows when the cannonball will strike the surface of the water is:

h(4) or h(t=4) = -16(4)^2 + 60(4) + 16 = -256 + 240 + 16 = 0

Therefore, the height of the cannonball will be 0 feet when it strikes the surface of the water after 4 seconds.