Question

Tom throws a ball into the air. The ball travels on a parabolic path represented by the equation , where represents the height of the ball above the ground and represents the time in seconds. The maximum value achieved by the function is represented by the vertex. Use factoring to answer the following: How many seconds does it take the ball to reach its highest point

Answer 1

2.5 second

Explanation:

The equation is missing in the question.

The equation is,
`h=-8t^2+40t` , where 'h' is the height and 't' is time measured in second.

Now we know to reach its maximum height, h in t seconds, the derivative of h with respect to time t is given by :

`(dh)/(dt) =0`

Now the differentiating the equation with respect to time t, we get

`(dh)/(dt)=(d)/(dt)(-8t^2+40t)`

`(dh)/(dt)=-16t+40`

For maximum height,
`(dh)/(dt) =0`

So,
`-16t+40=0`

`\Rightarrow 16t=40`

`\Rightarrow t=(40)/(16)`

`\Rightarrrow t = 2.5`

Therefore, the ball takes 2.5 seconds time to reach the maximum height.