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

Answer:

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

D is correct.

Step-by-step 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.

$h(t)=\dfrac{1}2gt^2+v_ot+h_o$

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.

Answer 2

Answer:

The correct option is the last option

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

Step-by-step explanation:

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

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

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:

$h(t) = 28 + 85t - \frac{1}{2}32.16t ^ 2$

Finally:

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

The correct option is the last option