Question

Arthur drops a ball from a height of 81 feet above the ground. it’s height, , is given by the equation h=16ft^2+81, where t is the time in seconds. for which interval of the time is the height of the ball less than 17 feet

Answer 1

The height of the ball is less than 17 feet for t > 2 seconds.

Explanation:

The height of the ball after t seconds is given by the following equation:

`h(t) = -16t^(2) + 81`

For which interval of the time is the height of the ball less than 17 feet

This is t for which:

`h(t) < 17`

So

`-16t^(2) + 81 < 17`

`16t^(2) < -64`

Multiplying by -1

`16t^(2) > 64`

`t^(2) > (64)/(16)`

`t^(2) > 4`

`t > √(4)`

`t > 2`

The height of the ball is less than 17 feet for t > 2 seconds.