Question

If a rocket in a field is fired straight upward with an initial velocity of 360 feet per second then its heightafter x seconds is given by the function: h() = −162 + 3601) Draw a rough sketch what this function might look like, i.e., the ground and the parabola of the rocket inthe air.2) Calculate how long will it take for the rocket to reach its highest point in the air.3) What is the highest point? (State the point.)4) How long will it take until the rocket hits the ground?5) What is the domain and range of this function?6) How far off the ground will the rocket be in 5 seconds?7) How far off the ground will the rocket be in 18 seconds?

Answer 1

y = -16x^2 + 360x

We want to find the vertex of the parabola

The h value is - b/2a = -360/ ( 2* -16) = -360 / -32 = 11.25

It will take 11.25 seconds for the rocket to reach the maximum height

The highest point is the y value when x = 11.25 seconds

y = -16 ( 11.25)^2 + 360(11.25)

= -16 (126.5625) +4050

=2025

The maximum height is 2025 ft

The zeros of the function is when the rocket is at the ground

0 = -16x^2 + 360x

Factor out 8x

0 = 8x ( -2x+45)

Using the zero product property

8x =0 -2x+45 =0

x=0 -2x = -45

x = -45/-2

x =22.5

The rocket will hit the ground at 22.5 seconds

The domain is the values that x can take. That is the time the rocket takes off until the time it hits the ground again

0 ≤ x ≤ 22.5 seconds

The range is the values that y can take

The values is when it is on the ground to the max at 2025

0 ≤ y ≤ 2025 ft

At 5 seconds x=5

y = -16 (5)^2 + 360(5)

= 1400 ft

At 18 seconds x = 18

y = -16 (18)^2 +360(18)

= 1296 ft