Calculus in Physics

Question

The position function for a falling objects is given by s(t)=−16t^2+v0t+s0, where s(t) is the height of the object in feet, v0 is the initial velocity, s0 is the initial height, and t is the time in seconds.

 

A ball is shot upwards from the surface of the earth (s0=0) with an initial velocity of 65 feet per second. What is the maximum height reached by the ball?

 

Round your answer to the nearest integer.

 

The maximum height reached by the ball is ____________.

Answer 1

Joaquin

The graph of the function is a quadratic, facing upwards.

The maximum height will be when t = -b/2a

a = -16, b = 65, c = 0

So solve for t, then substitute back into the function

Mike

Answer 2

Vy = Vyo -g*tmax ; Vy = 0 m/s at max height

-Vyo = -g*tmax

Tmax= Vyo/g

65 ft/sec = 32.174 ft/s2 *tmax

Tmax = 2.02 sec

S(t) = -16t^2 +65t

= -16(2.02)^2 +65(2.02)

=~ 66 ft