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The height of a free falling object at time t can be found using the function, h(t) = - 12t2 + 36t. Where h(t) is the height in feet and t is the in seconds. Find the time when the object hits the ground

Respuesta :

carlosego
For this case we have the following equation:
 h (t) = - 12t2 + 36t
 When the object hits the ground we have:
 - 12t2 + 36t = 0
 We look for the roots of the polynomial:
 t1 = 0
 t2 = 3
 Therefore, the time it takes the object to hit the ground is:
 t = 3 s
 Answer:
 the time when the object hits the ground is:
 t = 3 s

Answer:

3 seconds is the time when the object hits the ground.

Step-by-step explanation:

Given the height of a free falling object at time t can be found using the function is given by:

[tex]h(t)=-12t^2+36t[/tex]         ....[1]

where,

h(t) is the height in feet

t is the in seconds.

We have to find the time when the object hits the ground.

⇒h(t) = 0

Substitute this in [1] we have;

[tex]-12t^2+36t =0[/tex]

⇒[tex]12t^2-36t = 0[/tex]

⇒[tex]12t(t-3) = 0[/tex]

⇒t = 0 and t = 3

Since, time cannot be 0.

⇒t = 3 seconds

Therefore, the time when the object hits the ground is, 3 seconds

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