A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. it accelerates upward at 30.0 m/s2 for 30.0s, then runs out of fuel. ignore any air resistance effects. part a what is the rocket's maximum altitude?

There are two stages to the flight: acceleration stage and deceleration stage.

m₁ = 200 kg, mass of the rocket

m₂ = 100 kg, mass of fuel

a₁ = 30.0 m/s², upward acceleration when burning fuel

Ignore air resistance and assume g = 9.8 m/s².

Acceleration stage:

The rocket starts from rest, therefore the initial vertical velocity is zero.

The distance traveled is given by

s₁ = (1/2) * (30.0 m/s²) * (30.0 s) ² = 13500 m

Deceleration stage (due to gravity):

The initial velocity is u = (30.0 m/s²) * (30 s) = 900 m/s

The initial height is 13500 m

At maximum height, the vertical velocity is zero.

Let s₂ = the extra height traveled. Then

(900 m/s) ² - 2 * (9.8 m/s²) * (s₂ m) = 0

s₂ = 900²/19.6 = 41326.5 m

The maximum altitude is

s₁+s₂ = 54826.5 m

Answer: 54,826.5 m