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The height, h, of a thrown ball as a function of t, the amount of time

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The height, h, of a thrown ball as a function of t, the amount of time [#permalink] New post   16 Jun 2021, 02:05
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The height, h, of a thrown ball as a function of t, the amount of time it has been in the air, is given by \(h(t) = –10t^2 + 40t\). What is the maximum height attained by the ball?


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Pranaygre
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The height, h, of a thrown ball as a function of t, the amount of time [#permalink] New post   16 Jun 2021, 02:57
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given
\(h(t)=–10t^2+40th(t)=–10t^2+40t\)

for getting maximum height differentiate the equation on both sides

-20t+40 = 0
t = 2
maximum height will be attainted at t=2sec

so h=80-40=40

option C is correct
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arjunbir
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Re: The height, h, of a thrown ball as a function of t, the amount of time [#permalink] New post   18 Jun 2021, 05:02
I still did not get the explanation. Can someone please explain the solution in detail?
thanks
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Re: The height, h, of a thrown ball as a function of t, the amount of time [#permalink] New post   18 Jun 2021, 07:56
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Hey,

This is an easy one but only if you know differentiation. Let's try the other way.

Consider it as a quadratic equation. h(t)=\(–10t^2+40t\)

It's an equation of parabolic curve. The vertex of the parabola will be the maximum height achieved by the ball.

The general form for a quadratic equation is ax² + bx + c, here \(a\) is \(-10\), and \(b\) is \(40\)
Now maximum height will occur at \(t = \frac{-b}{2a}\)

\(t = \frac{-40}{-20} = 2\)

Put the value in the original equation,

h(2)=\(–10(2)^2+40(2)\) = 40

Maximum height = 40

Answer C

Please refer this for any doubts : https://brainly.com/question/12298041


arjunbir wrote:
I still did not get the explanation. Can someone please explain the solution in detail?
thanks
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