Answer:
The velocity is 4.094ft/s
Step-by-step explanation:
Given
[tex]s(t) = -3t^2+100t+3[/tex]
[tex]s(t) = 131[/tex]
Required
Find the velocity at 131ft
First, calculate the time taken to reach 131 ft
[tex]s(t) = -3t^2+100t+3[/tex]
This gives:
[tex]131 = -3t^2 + 100t + 3[/tex]
Rewrite as:
[tex]3t^2 - 100t - 3 + 131 = 0[/tex]
[tex]3t^2 - 100t +128 = 0[/tex]
Expand
[tex]3t^2 - 96t - 4t + 128 = 0[/tex]
Factorize
[tex]3t(t - 32) -4(t -32) = 0[/tex]
Factor out t - 32
[tex](3t - 4)(t -32) = 0[/tex]
Split
[tex]3t - 4 =0\ or\ t - 32 = 0[/tex]
Solve for t
[tex]t = \frac{4}{3}\ or\ t =32[/tex]
Since 32 > 4/3, then the flare is going up at 4/3s and coming down at 32s
The velocity is calculated as:
[tex]v = \frac{s}{t}[/tex]
So, we have:
[tex]v = \frac{131}{32}[/tex]
[tex]v = 4.094[/tex]