Question

A ball is thrown at an initial height of 7 feet with an initial upward velocity at 27 ft/s. The balls height h (in feet) after t seconds is give by the following. h- 7 27t -16t^2 Find the values of t if the balls height is 17ft. Round your answer(s) to the nearest hundredth

Answer 1

The height of ball is 17 ft at t=0.55 and t=1.14.

Explanation:

The general projectile motion is defined as

`y=-16t^2+vt+y_0`

Where, v is initial velocity and y₀ is initial height.

It is given that the initial height is 7 and the initial upward velocity is 27.

Substitute v=27 and y₀=7 in the above equation to find the model for height of the ball.

`h(t)=-16t^2+27t+7`

The height of ball is 17 ft. Put h(t)=17.

`17=-16t^2+27t+7`

`0=-16t^2+27t-10`

On solving this equation using graphing calculator we get

`t=0.549,1.139`

`t\approx 0.55,1.14`

Therefore the height of ball is 17 ft at t=0.55 and t=1.14.