Answer to Question #143803 in Calculus for ava loss

Question

The equation for a projectile's height versus time is n(t) = -1662 +V++ to
A tennis ball machine serves a ball vertically into the air from a height of 2
feet, with an initial speed of 120 feet per second. What is the maximum
height, in feet, the ball will attain?
Round to the nearest whole foot.

Answer 1

h(t)= -16t^2+ ut +ho,

Where u is the initial speed

ho=2, u=120.

Substitute these values into the function

h(t)= -16t^2+ 120t + 2.

Take the first derivative of h(t)

h’(t) = -16*2t + 120, 

h'(t)= -32t +120.

Equate the derivative with zero

h’(t)= 0.

Solve the equation -32t +120 = 0.

-32t = -120t=, t= -120/(-32)

 t= 3.75s.

Find the maximum height the ball will attain t=3.75s,  

h(3.75) = -16 (3.75)^2 + 120 *3.75 +2.

=-225+ 450 +2= 227ft.

Answer: 227ft.