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OverLord2011 [107]
3 years ago
6

A ball is thrown into the air and its position is given by h ( t ) = − 6.3 t 2 + 53 t + 24 where h is the height of the ball in

meters t seconds after it has been thrown. Find the maximum height reached by the ball and the time at which that happens.
Mathematics
1 answer:
nordsb [41]3 years ago
8 0

Answer:

h'(t) = -12.6 t +53

Now we can set up the derivate equal to 0 and we have:

-12.6 t +53 = 0

And solving for t we got:

t = \frac{53}{12.6}= 4.206

For the second derivate respect the time we got:

h''(t) = -12.6

So then we can conclude that t = 4.206 is a maximum for the function.

And the corresponding height would be:

h(t=4.206) = -6.3(4.206)^2 +53*4.206+24= 135.468 ft

So the maximum occurs at t = 4.206 s and with a height of 135.468 m

Step-by-step explanation:

For this case we have the following function:

h(t) = -6.3t^2 +53 t+24

In order to maximize this function we need to take the first derivate respect the time and we have:

h'(t) = -12.6 t +53

Now we can set up the derivate equal to 0 and we have:

-12.6 t +53 = 0

And solving for t we got:

t = \frac{53}{12.6}= 4.206

For the second derivate respect the time we got:

h''(t) = -12.6

So then we can conclude that t = 4.206 is a maximum for the function.

And the corresponding height would be:

h(t=4.206) = -6.3(4.206)^2 +53*4.206+24= 135.468 ft

So the maximum occurs at t = 4.206 s and with a height of 135.468 m

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