Question

The height in feet of a golf ball hit into the air is given by `h= -16t^2 + 64t`, where t is the number of seconds elapsed since the ball was hit. What is the maximum height of the ball?

Answer 1

`64` feet

Explanation:

`h = -16 t^2 + 64 t`

maximum or minimum height when `h' =0`

`h' = -32 t + 64`

when `h' =0, -32 t + 64 =0`

`32 t = 64`, `t = 64/32 = 2`

`h'' = -32`, and since `h''` has a -ve value, therefore `h` is maximum when `t = 2`

when t =2,
`h = -16 (2)^2 + 64 (2)`
`h = -16 (2)^2 + 64 (2)`
`h = -16 (4) + 64 (2) = -64 + 128 = 64`

Answer 2

`64" feet"`

Explanation:

Find the roots of the parabola by setting h = 0

`rArr-16t^2+64t=0`

Factorising gives.

`-16t(t-4)=0`

`rArrt=0" or " t=4`

Since the parabola is symmetrical the axis of symmetry will pass through the maximum. The axis of symmetry is positioned at the mid- point of the roots.

`rArrcolor(red)(t=2)`

`rArr"max. height "=-16color(red)((2))^2+64(color(red)(2))`

`color(white)(xxxxxxxxxxxx)=(-16xx4)+(64xx2)`

`color(white)(xxxxxxxxxxxx)=-64+128`

`color(white)(xxxxxxxxxxxx)=64`

`rArr"maximum height of ball " =64" feet"`