Rocket's Max Altitude & Time in Air

[Mirole]

Homework Statement

A 200kg weather rocket is loaded with 100kg of fuel and fired straight up. It accelerates upward at 35m/s^2 for 32 s, then runs out of fuel. Ignore any air resistance effects.

What is the rocket's maximum altitude?
How long is the rocket in the air?

Homework Equations

Vf^2=Vi^2-2as
Vf=Vi+at

The Attempt at a Solution

Vf=0+(35)(32)
Vf=1120m/s

1120=0+2(35)s
1234400=70s
s=133.865m

I think I'm supposed to add the weight in, but I'm not sure on how to do that.

 

[D H]

I think you are supposed to use the fact that it "accelerates upward at 35m/s^2 for 32 s, then runs out of fuel".

 

[Mirole]

I think you are supposed to use the fact that it "accelerates upward at 35m/s^2 for 32 s, then runs out of fuel".

The problem is I'm not sure if I got the velocity for the first part right, I know you would include gravity during the part after the fuel runs out and it would be decreasing until it hit the turning point and started falling.

 

[D H]

Do try to get your algebra straight at least (you have some serious goofs in the original post).

Here's a clue on how to solve problems like these; this approach applies to many, many other problems in science. Break the problem down into smaller, more manageable pieces, solve each piece, and at the end put the pieces back together.

What are the pieces in this problem?

1. The rocket accelerates upwards at 35m/s^2 for 32 seconds.
2. The rocket continues going up, but slows down because of gravity. Eventually its upward velocity slows to zero ...
3. at which point it falls earthward and eventually hits the earth.

See if you can determine the height, velocity, and time at the end of these intervals.