In the year 2055, a rocket was launched from a research laboratory on Mars. Mars has essentially no atmosphere. The test rocket had an initi

Question

In the year 2055, a rocket was launched from a research laboratory on Mars. Mars has essentially no atmosphere. The test rocket had an initial acceleration of 8.0 m/s2. Its engine burned for 7.00 seconds, and then the rocket coasted in a condition of free fall, under the influence of Mars’s gravity, which is 3.71 m/s2. Find the maximum height reached by the rocket.

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Lệ Thu 4 years 2021-07-28T01:14:41+00:00 1 Answers 9 views 0

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  1. Sigrid
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    2021-07-28T01:15:54+00:00
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    Answer:

    h = 618.64 m

    Explanation:

    First we need to calculate the height gained by rocket while the fuel is burning. We use 2nd equation of motion for that purpose:

    h₁ = Vit + (1/2)at²

    where,

    h₁ = height gained during the burning of fuel

    Vi = Initial Velocity = 0 m/s

    t = time = 7 s

    a = acceleration = 8 m/s²

    Therefore,

    h₁ = (0 m/s)(7 s) + (1/2)(8 m/s²)(7 s)²

    h₁ = 196 m

    Now we use 1st equation of motion to find final speed Vf:

    Vf = Vi + at

    Vf = 0 m/s + (8 m/s²)(7 s)

    Vf =  56 m/s

    Now, we calculate height covered in free fall motion. Using 3rd equation of motion:

    2ah₂ = Vf² – Vi²

    where,

    a = – 3.71 m/s²

    h₂ = height gained during free fall motion = ?

    Vf = Final Velocity = 0 m/s (since, rocket will stop at highest point)

    Vi = 56 m/s

    Therefore,

    (2)(-3.71 m/s²)h₂ = (0 m/s)² – (56 m/s)²

    h₂ = 422.64 m

    So the total height gained will be:

    h = h₁ + h₂

    h = 196 m + 422.64 m

    h = 618.64 m

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