Question

The height of an object t seconds after it is thrown from a height of h feet is modelled by the equation h(t) = -16t^2 + vt + h. If the ball is thrown from a point 6 feet above ground with an initial velocity, v, of 30 feet per second, how long will it take for the ball to hit the ground???​

Answer 1

At 0.713 second the ball will hit the ground

Explanation:

The height of an object t seconds after it is thrown from a height of h feet is modeled by the equation:

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

The ball is thrown from a point 6 feet above ground with an initial velocity, v, of 30 feet per second, equation becomes:

`h(t) = -16t^2 + 3t + 6`

It is required to find the time when the ball hits the ground. At that point, h(t) =0.

So,

`-16t^2 + 3t + 6=0`

Above is a quadratic equation, the value of time is given by :

t = -0.526 s and t = 0.713 seconds

So, at 0.713 second the ball will hit the ground.