Question

ball is thrown 40 meters above ground. the height of the ball from the ground level after t seconds is defined by using the function h(t)=40t-5t^2. how long will the ball take to hit the ground

Answer 1

Answer:

The ball will take 8.90 seconds to hit the ground.

Step-by-step explanation:

The height of a ball after t seconds is given by:

$h(t)=40t-5t^2$

Determine how long will the ball take to hit ground level. Since the gound is 40 meters below the throwing point:

$40t-5t^2=-40$

Rearranging:

$5t^2-40t-40=0$

Simplifying by 5:

$t^2-8t-8=0$

Solving the quadratic equation with the formula:

$\displaystyle t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

With a=1, b=-8, c=-8

$\displaystyle t=\frac{8\pm \sqrt{64+32}}{2}$

$\displaystyle t=\frac{8\pm \sqrt{96}}{2}$

There are two solutions:

t=8.90 sec, t=-0.90 sec

Due to the nature of the problem, t cannot be negative, thus:

The ball will take 8.90 seconds to hit the ground.