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Ksenya-84 [330]
3 years ago
10

A rocket is launched into the air and follows the path, h(t) = -3t^2 + 12t, where t is time measured in seconds. Determine how l

ong it takes the rocket to hit the ground. Show all work for full credit.

Mathematics
2 answers:
vodka [1.7K]3 years ago
8 0
Note that height is equal to 0 when time equals 0 and when time equals 4, but we are only concerned with time equal to 4

Marina86 [1]3 years ago
6 0

Answer:

4 seconds

Step-by-step explanation:

Given: A rocket is launched into the air and follows the path,\text{h}(\text{t})=-3\text{t}^2+12\text{t}, where t is time measured in seconds

To Find: how long it takes the rocket to hit the ground

Solution:

Path followed by rocket

\text{h}(\text{t})=-3\text{t}^2+12\text{t}

here, t is time in seconds and h is height

height of rocket  when it hit ground,

\text{h}=0\text{m}

putting value of h in equation

0=-3\text{t}^2+12\text{t}

3\text{t}^2-12\text{t}=0

3\text{t}(\text{t}-4)=0

\text{t}=0,4

height of rocket will be 0 at time t=0s and t=4s

\text{t}=0 , time when rocket is launched

\text{t}=4 , time when rocket hits ground

Total time taken to hit the ground=4-0=4\text{s}

Time taken by rocket to hit the ground is 4 seconds.

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