Question

A rocket is launched at 85 ft./s from a launch pad that’s 28 feet above the ground. which equation can be used to determine the height of the rocket at a given time after the launch? (answer choices in picture)

Answer 1

The correct option is the last option

`h(t) = 28 + 85t -16t ^ 2`

Explanation:

The kinematic equation to calculate the position of a body on the vertical axis as a function of time is:

`h(t) = h_o + v_ot - (1)/(2)gt ^ 2`

Where:

`h_0` = initial position = 28ft

`v_0` = initial velocity = 85 ft / s

g = acceleration of gravity = 32.16ft / s ^ 2

Then the equation sought is:

`h(t) = 28 + 85t - (1)/(2)32.16t ^ 2`

Finally:

`h(t) = 28 + 85t -16t ^ 2`

The correct option is the last option

Answer 2

`h(t)=-16t^2+85t+28` is equation of height of rocket at given time after the launch.

D is correct.

Explanation:

A rocket is launched at 85 ft./s from a launch pad that’s 28 feet above the ground

We have an equation of rocket launching.

`h(t)=\frac{1}2gt^2+v_ot+h_o`

Where, g is acceleration due to gravity

v is initial velocity

h is initial height

h(t) is function of height at any time t

A rocket is launched by 85 ft/s

`V_o=85\ ft/s`

`g=-32\ ft/s`

`h_o=28`

Substitute the value into formula ans get formula

`h(t)=-16t^2+85t+28`

Hence, D is correct. Equation of height of rocket at given time after the launch.