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.

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