Finding time using Impulsive forces and momentum

[WarOwk]

Homework Statement

A rocket, weighing 43,600N, has an engine that provides an upward force of 120,000N. It reaches a maximum speed of 860 m/s. For how much time must the engine burn during launch in order to reach this speed?

Homework Equations

p=m*Δv
i=F*t

The Attempt at a Solution

I started by using 120,000N as the Force. I used 43,600 as the mass and 860 as the velocity. I multiplied 43,600 by 860 to get 37,496,00. I then divided the momentum(37,496,000) by the force(120,000) to solve for time. The solution I got was 312.5 seconds. Our teacher has already given us the answer to the problem which is 31.8 seconds, but there is an upcoming test and I would like to know how he got this answer.

 

[George Jones]

Clue: 312.5/31.8 = 9.8

 

[WarOwk]

Clue: 312.5/31.8 = 9.8

I think I figured it out. Momentum is measured in kg*m/s, but the mass is measured in Newtons. So, you divide the 312.5 by 9.8 to get it in correct units. When I divided the 43,600 N first I got the same answer. The quote helped. Thank You!

 

[George Jones]

but the mass is measured in Newtons.

Weight is measured in Newtons; mass is measured in kilograms.

 

[WarOwk]

I think I understand it now, weight is the gravitational force of an object. It's equation is (9.8N/kg * mass), and mass is the weight divided by 9.8 N/kg because it is the amount of stuff on an object. Mass and weight are inversely related to each other.

 

[haruspex]

mass is the weight divided by 9.8 N/kg

Yes, but that is not how mass is defined. "Mass" generally means inertial mass and is defined as resistance to linear acceleration. If a firce F is applied to a mass and the resulting acceleration is a then the mass is F/a.
It turns out that inertial mass is proportional to gravitational mass, but there is no known reason the universe had to be that way.

Mass and weight are inversely related to each other.

No, directly proportional, not inversely.