Question
A $5.00 \times 10^5 \textrm{ kg}$ rocket is accelerating straight up. Its engines produce $1.250 \times 10^7 \textrm{ N}$ of thrust, and air resistance is $4.50 \times 10^6 \textrm{ N}$. What is the rocket’s acceleration? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

$6.20 \textrm{ m/s}^2$

Solution Video

# OpenStax College Physics Solution, Chapter 4, Problem 23 (Problems & Exercises) (1:36) View sample solution

## Calculator Screenshots Video Transcript

This is College Physics Answers with Shaun Dychko. One of the best ways to prepare any of your solutions is to draw a picture. So that's what I've done here. This is especially important for forces or dynamics questions because you need to draw the free body diagram to show all the forces involved. So with this rocket we have a thrust force upwards of 1.25 times ten to the seven newtons and then downwards we have gravity and then we also have the air resistance which is directed opposite to the direction of motion and so that will be downwards as well because the rocket is moving up. So the air friction down is 4.5 times ten to the six newtons. We're told that the mass of the rocket is 5 times ten to the five kilograms and so we've drawn a free body diagram and written down everything that we know. Then we can proceed to the algebra which is that the net force is the up force, up forces minus the down forces, and so we have up as the thrust force and then minus each of the down forces, air and gravity. That net force equals mass times acceleration. Gravity is <i>mg</i>. So we'll divide both sides by <i>m</i> here and then substitute for <i>fg</i> and we get this line here, acceleration is thrust, minus air resistance, minus <i>mg</i> weight, divided by the mass, <i>m</i>. We substitute each of those numbers in here and we end up with 6.2 meters per second squared as the acceleration of the rocket.

Submitted by hphillips32 on Wed, 06/24/2020 - 09:53

i don't understand how you got the answer

Submitted by ShaunDychko on Wed, 06/24/2020 - 11:43

Hello, in case it was confusing, the calculator screenshot was the wrong one. I have updated it with the correct screenshot. Otherwise, the main idea for this solution is to divide the net force by the mass to find the acceleration. Net force is the result of adding/subtracting all the forces.
All the best,
Shaun