A firecracker is fired from the ground. The height of the firecracker at a given time is modelled by the function `h(t)=-5t^2+50t` , where h(t) is the height in metres and t is time in seconds. When will the firecracker reach a height of 45m?

Expert Answers

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`h(t)= -5t^2 + 50t` .

We need to find the time needed for the firecracker to reach a height of 45m.

Then we will subsitute with h(t)= 45

==> -5t^2 + 50t = 45

==> `-5t^2 + 50t - 45 =`  0

Now we will factor -5:

==> `-5(t^2- 10t +9) = ` 0

Now divide by -5.

==> `t^2- 10t+ 9 =`  0

Now we will solve the quadratic equation for t.

we will factor.

==> (t-1)(t-9) = 0

==> t1= 1

==> t2= 9

Then there are two answers.

The firecracker will be at height 45 m after t1=1 second, and then again after t2=9 seconds when the firecracker is falling toward the ground.


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