- 16

- 1

**1. Homework Statement**

A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 30 m/s^2 for 30s, then runs out of fuel. Ignore any air resistance effects. What is the rocket’s maximum altitude?

**2. Homework Equations**

Δx=V

_{0}t+(1/2)at

^{2}

V=V

_{0}+at

2aΔx=V

^{2}-V

_{0}

^{2}

**3. The Attempt at a Solution**

Δx=(1/2)(30m/s

^{2})(30s)

^{2}=13500m

V=0(m/s)+(1/2)(30m/s

^{2})(30s)=900m/s

2(-9.81m/s

^{2})Δx=0

^{2}-900

^{2}m/s

=> Δx=41300m

Total height: 55000m

However, I did it another way and received a different result.

V=V

_{0}+at

0=900+(-9.81)t

t=91.7s

Δx=(900m/s)(91.7s)=82530m

Total height: 96000m

Why is this?