Question

Task 1:
Your nephew is standing on his deck, which is 4 feet off the
ground. He tosses his toy up into the air at an initial velocity
of 7 feet per second. The equation h = -2t2 + 7+ + 4 models
the toy's height hin feet from the ground at t seconds after
he threw it.
What is the toy's maximum height?​

Answer 1

Answer:

The toy's maximum height is $10.12\ \text{feet}$.

Step-by-step explanation:

The equation that models the toy's height in feet from the ground at t seconds after  he threw it is given by :

$h = -2t^2 + 7t + 4$ .....(1)

It is required to find the toy's maximum height. For maxima or minima, put

$\dfrac{dh}{dt}=0$

Plugging the value of t in above equation,

$\dfrac{d(-2t^2 + 7t + 4)}{dt}=0\\\\-4t+7=0\\\\t=\dfrac{7}{4}\\\\t=1.75\ s$

Now put t = 1.75 s in equation (1) such that,

$h = -2(1.75)^2 + 7(1.75) + 4\\\\h=10.12\ \text{feet}$

So, the toy's maximum height is $10.12\ \text{feet}$.

Answer 2

The toy's maximum height is 10.12 feet.

Calculation of the  toy's maximum height:

Since the nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air at an initial velocity of 7 feet per second. The equation is $h = -2t^2 + 7+ 4$

So first we have to determine the t i.e.

$d(-2t^2 + 7 +4) \div dt = 0\\\\-4t + 7 = 0\\\\ t = 7\div 4$

t = 1.75 s

Now

the height should be

$= -2(1.75)^2 + 7(1.25)+ 4$

= 10.12 feet.

hence, The toy's maximum height is 10.12 feet.

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