calculus question

Question

You hit a golfball vertically upward with your pitching wedge. The position function of the ball is s(t) = -3t^2+30t where the origin is at ground level and the positive direction is vertically upward. (Distance is in metres). Help!?

 

A) Find the maximum height reached by the ball
B) Find the velocity of the ball as it reaches the ground
C) Find the acceleration of the ball.

Answer 1

s(t) = -3t² + 30t

 

(A)

 

Set ds/dt = 0, solve for t, and plug into s(t)

 

ds/dt = -6t + 30 = 0 ⇒ t = 5

 

s_max = s(5) = -3(5²) + 30(5) = 75 m

 

(B)

 

v(t) = ds/dt = -6t + 30

 

It reaches the ground when s(t) = 0

 

s(t) = 3t(-t + 10) = 0 ⇒ t = 10  [t = 0 is moment of launch]

 

v(10) = -6(10) + 30 = -30 m/s  [the minus sign means it is moving downward, which makes sense]

 

(C)

 

a = dv/dt = -6 m/s²