The height in feet of a bottle rocket in given by h(t)=160t-16t^2 where t is the time in seconds. How long will it take for the rocket to re

Question

The height in feet of a bottle rocket in given by h(t)=160t-16t^2 where t is the time in seconds. How long will it take for the rocket to return to ground ? What is the height after 2 secs? HELP ME PLEASE!!!!!!!!! Please show workkkkkk!!!!

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Maria 2 weeks 2021-11-18T06:33:56+00:00 1 Answer 0 views 0

Answers ( )

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    2021-11-18T06:35:42+00:00

    a) 10 sec

    b) 256 feet

    Step-by-step explanation:

    a)

    The height of the rocket above the ground at time t is described by the second-order equation

    h(t)=160t-16t^2 (1)

    where:

    t is the time, in seconds

    h(t) is the height, in feet

    160 represents the initial vertical velocity of the rocket

    -16 represents the acceleration due to gravity (downward)

    The rocket will return to the ground when the height is zero, so when

    h(t)=0

    Substituting into eq(1) and solving for t, we find:

    0=160t-16t^2\\0=16t(10-t)=0

    which has two solutions:

    t = 0 (initial instant, so when the rocket starts its motion)

    t = 10 s –> this is the time at which the rocket returns to the ground

    b)

    The height of the rocket is given by

    h(t)=160t-16t^2

    t is the time, in seconds

    h(t) is the height, in feet

    Here we want to find the height of the rocket after 2 seconds: to do that, we just need to substitute

    t = 2 sec

    into the equation of the height.

    By doing so, we find:

    h(2)=160\cdot 2 -16(2)^2=256 ft

    Therefore, the height of the rocket after 2 seconds is 256 feet.

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