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.

Option D is correct.

Step-by-step explanation:

Given: A rocket is launched with speed 85 ft/s from a height 28  feet.

Launching a rocket follows the path of parabola. The equation of rocket should be parabolic.

Parabolic equation of rocket is

Formula: $h(t)=\dfrac{1}2gt^2+v_0t+h_0$

g ⇒ acceleration due to gravity (-32 ft/s)

v ⇒ Initial velocity ($v_0=85\ ft/s$)

h ⇒ Initial height ($h_0=28\ feet$)

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

Substitute the given values into formula

$h(t)=\frac{1}{2}(-32)t^2+(85)t+28$

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

D is correct.

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 = $85\ \frac{ft}{s^2}$

g = acceleration of gravity = $32.16\ \frac{ft}{s} ^ 2$

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