Question

The function H(t) = −16t2 + 75t + 25 shows the height H(t), in feet, of a baseball after t seconds. Part A: After how many seconds does the baseball hit the ground? You do not need to show your work. Part B: What is the maximum height of the baseball? You do not need to show your work.

Answer 1

Step-by-step explanation:

Given that,

The function that shows the height of a baseball after t seconds is given by :

$H(t)=-16t^2+75t+25$ ....(1)

Part (A).

When the baseball hits the ground,

H(t) = 0

So,

$-16t^2+75t+25=0\\\\t=5\ s\ and\ t=-0.31\ s$

After 5 seconds the baseball will hit the ground.

Pat (B)

For maximum height, put dH/dt = 0

So,

$\dfrac{d}{dt}(-16t^2+75t+25)=0\\\\-32t+75=0\\\\t=2.34\ s$

Put t = 2.34 s in equation (1).

$H(t)=-16(2.34)^2+75(2.34)+25\\\\H(t)=112.89\ m$

Hence, this is the required solution.