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.

A & C

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

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

USe quadratic formula to solve for t

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

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

At t=0 , h(0) = 5

Answer 2

Answer:

Step-by-step explanation:

In the equation, 72t represents the initial upwards velocity and 5 represents the initial launching height.  The leading term represents the pull of gravity on the object in the English system of measurement.

So the first question says the initial height is 5 feet.  TRUE

The second question says the initial vertical velocity is -72.  FALSE (it's positive 72 ft/sec)

The third question says that the object will hit the ground after approximately 4.57 seconds.  TRUE.  Find this by setting the h(t) on the left equal to 0, since this is the height at any time during the flight.  When h(t) = 0, that means that there is NO height, which means the object is on the ground.  Set the equation equal to 0 and factor to find t.  Putting that into the quadratic formula gives you t values of -.068 and 4.57.  Since the 2 things in math that will NEVER EVER be negative are distances and time, we can safely disregard the negative t value and go with t = 4.57.

The fourth question says that after t = 3 seconds, the object is 173 feet high.  FALSE.  Find this by subbing in a 3 for every t in the equation.

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

This gives you that h(3) = 77 feet

The last question says that at t = 0, h(t) = 0.  FALSE again.  Sub in a 0 for every t in the equation, and you get h(0) = 5, which is the initial launching height.