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A coin is tossed upward with an initial velocity of 32 feet per second from a height of 16 feet above the ground.The equation giving the object's height h at any time t is h = 16 + 32t - 16t^2. Does the object ever reach a height of 32 feet?(Select an answer No or Yes! If so, when? (Answer "dne" if it does not.)It reaches 32 feet after___seconds.

A coin is tossed upward with an initial velocity of 32 feet per second from a height of 16 feet above the groundThe equation giving the objects height h at any class=

Respuesta :

Solution:

Given:

[tex]h=16+32t-16t^2[/tex]

To get the maximum height, we differentiate. At maximum height, the velocity is zero.

Hence,

[tex]\begin{gathered} \frac{dh}{dt}=32-32t \\ when\text{ }\frac{dh}{dt}=0, \\ 0=32-32t \\ 32t=32 \\ t=\frac{32}{32} \\ t=1sec \end{gathered}[/tex]

Thus, substitute t = 1 into the equation;

[tex]\begin{gathered} h=16+32(1)-16(1^2) \\ h=16+32-16 \\ h=32ft \end{gathered}[/tex]

Since the maximum height is 32 feet, then the object reaches 32feet after 1 second.

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