Question

A golfer strikes a golf ball into the air from the ground. The height, h metres, of the ball

Answer 1

Answer:

64 m, at time t = 4 sec

Step-by-step explanation:

We must maximize the function h = 32t – 4t^2.  One way in which to do this is to find the axis of symmetry, t = -b / [2a], and from that calculate the height:

a = -4, b = 32, c = 0

                                                                          -32

and therefore the axis of symmetry is t = ---------------- = 4

                                                                          2(-4)

The height, h, at time t = 4, is h(4) = 32(4) - 4(4)^2 = 64 m

The maximum height of the ball is 64 m, at time t = 4 sec

Answer 2

Step-by-step explanation:

The golf ball reaches its maximum vertical height when its vertical velocity h' becomes zero. Taking the derivative of h and setting it to zero, we get

h' = 32 - 8t = 0

which gives us t = 4 seconds. So after 4 seconds, the ball will reach its maximum height and its value is

h = 32(4) - 4(4)^2

= 128 - 64

= 64