rates of change

Question

You hit a golfball 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 up. (distance is in meters)

 

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

a) the max heght is at the vertex, so t = -b/(2a) = 30/6 = 5 seconds. so max ht is s(5); you can compute that.

 

b) velocity when hits ground will be s'(10).  differentiate s(t) & substitute t=10 for this computation.  why t=10? because of symmetry of the parabola...5 sec to vertex, 5 sec back down to ground since 'launch' was from ground level.

 

c) a(t) = s"(t) = -6 m/sec²