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nexus9112 [7]
3 years ago
12

Tom throws a ball into the air. The ball travels on a parabolic path represented by the equation , where represents the height o

f 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
Mathematics
1 answer:
tigry1 [53]3 years ago
7 0

Answer:

2.5 second

Step-by-step 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 :

\frac{dh}{dt} =0

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

\frac{dh}{dt}=\frac{d}{dt}(-8t^2+40t)

\frac{dh}{dt}=-16t+40

For maximum height,  \frac{dh}{dt} =0

So, -16t+40=0

 \Rightarrow 16t=40

\Rightarrow t=\frac{40}{16}

\Rightarrrow t = 2.5

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

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