Question

A rocket is launched from the top of a platform 50 feet above the ground. The rocket will fall after exploding at its maximum height. The rocket's height above the ground is given by the function h(r) = −16r2 + 64r + 50.

The function g(r) is shown in the graph.

graph with r on the x axis and g of r on the y axis that is increasing from the left going through about negative 8 and one half comma 0 to negative 4 comma 100 and then decreasing through negative 1 comma 55 and continuing down and to the right

Which function has the greater maximum?

a
h(r)

b
g(r)

c
h(r) and g(r) have the same maximum.

d
h(r) and g(r) do not have a maximum.

Answer 1

The maximum height that the rocket will reach is 271 feet.

Explanation:

We first calculate the time, t it takes the rocket to reach maximum height from v = u - gt. Since u = initial velocity = 128 ft/s, v = velocity at maximum height = 0 ft/s and g = acceleration due to gravity = 32 ft/s².

So, v = u - gt.

t = (u - v)/g

= (128 ft/s - 0 ft/s)/32 ft/s²

= 128 ft/s ÷ 32 ft/s²

= 4 s.

We calculate the maximum height from

y - y₀ = ut - 1/2gt² where y₀ = 15 ft and all other variables are as above.

Substituting these values into the equation, we have

y - y₀ = (u - 1/2gt)t

y - 15 ft = (128 ft/s - 1/2 × 32 ft/s² × 4 s) × 4 s

y - 15 ft = (128 ft/s - 64 ft/s)4 s

y - 15 ft = 64 ft/s × 4 s

y - 15 ft = 256 ft

y = 256 ft + 15 ft

y = 271 ft

So, the maximum height that the rocket will reach is 271 feet.

Explanation: