Question

An object is launched into the air. The projectile motion of the object can be modeled using the function h(t) = –16t2 + 72t + 5, where t is the time in seconds since the launch and h(t) represents the height in feet of the object after t seconds. What is true about the projectile motion of this object? Check all that apply.
The initial height is 5 feet.
The initial velocity of the object is –72 feet/second.
The object will hit the ground after approximately 4.57 seconds.
After 3 seconds, the object is 173 feet high.
At t = 0, h(t) = 0.

Answer 1

Answer:

The initial height is 5 feet.

The object will hit the ground after approximately 4.57 seconds.

Step-by-step explanation:

An object is launched into the air. The projectile motion of the object can be modeled using the function h(t) = -16t^2 + 72t + 5, where t is the time in seconds since the launch and h(t) represents the height in feet of the object after t seconds

General equation is

$h(t)= -16t^2 + v_0t+h_0$

V_0 is the initial velocity

h_0 is the initial height

From the given equation , the initial height is 5 feet

Initial velocity is +72 feet / sec

When the onbject hits the ground, the height becomes 0

So we plug in 0 for h(t) and solve for t

$0 = -16t^2 + 72t + 5$

USe quadratic formula to solve for t

$t= \frac{-b+-\sqrt{b^2-4ac} }{2a}$

a=-16, b= 72, c= 5

$t= \frac{-72+-\sqrt{72^2-4(-16)(5)} }{2(-16)}$

t= -0.06  and t= 4.568

The object will hit the ground after approximately 4.57 seconds.

To find out the height after 3 seconds, plug in 3 for t

$h(t) = -16(3)^2 + 72(3) + 5=77$

At t=0 , h(0) = 5

Answer 2

The initial height is 5 feet and the object will hit the ground after approximately 4.57 seconds.

At zero time of motion

When the time of motion is zero, the initial height of the object is calculated as follows;

h(t) = –16t2 + 72t + 5

h(0) = 0 + 5

h(0) = 5 ft

Time of motion of the object

The time of motion of the object is calculated as follows;

-16t² + 72t + 5 = 0

a = -16, b = 72, c = 5

solve the equation using formula method;

t = 4.57 s

Thus, the  true statement about the projectile motion of the object is the initial height is 5 feet and the object will hit the ground after approximately 4.57 seconds.

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