Free Fall/Constant Acceleration Problem

[cheerspens]

Homework Statement

A rocket is fired vertically and ascends with a constant vertical acceleration of 20.0 m/s^2 for 2.00 seconds. Its fuel is then used up and it continues as a free object. What is the maximum altitude reached?

Homework Equations

X=Xo+Vot+(1/2)at^2
V=Vo+at
2a(X-Xo)=V^2-Vo^2

The Attempt at a Solution

I don't know how to solve for the point at which the rocket runs out of fuel. Once I can do that I think I will be able to find the maximum altitude reached as it asks in the problem.

 

[Pengwuino]

They tell you at what time the rocket runs out of fuel. Use this to determine the height and velocity that the rocket is at when the fuel runs out.

 

[kerimek]

I would approach this problem by first breaking it down into smaller parts. The first part is the rocket's ascent with constant acceleration, which can be solved using the equations X=Xo+Vot+(1/2)at^2 and V=Vo+at. From this, we can calculate the rocket's velocity at the point when its fuel runs out, which will be 40 m/s.

Next, we can use the equation 2a(X-Xo)=V^2-Vo^2 to solve for the distance traveled by the rocket during the 2 seconds of constant acceleration. This will give us the initial height of the rocket when it becomes a free object.

From there, we can use the equation V^2=Vo^2+2a(X-Xo) to calculate the maximum height reached by the rocket as a free object. This will give us the final answer to the problem.

It is important to note that this solution assumes a few things, such as no air resistance and a constant acceleration due to gravity. In real-world scenarios, there may be other factors to consider which could affect the rocket's maximum altitude.