---
title: Midair Propulsion
topic: Kinematics(2D and 3D)
author: Tarek Alkabbani
source: original
template_version: 1.4
attribution: standard
partialCredit: true
singleVariant: false
showCorrectAnswer: false
outcomes:
- 5.5.1.1
- 5.5.1.3
difficulty:
- undefined
randomization:
- undefined
taxonomy:
- undefined
span:
- undefined
length:
- undefined
tags:
- APSC181
- TA
assets:
- Midair Propulsion.png
part1:
type: number-input
pl-customizations:
rtol: 0.05
weight: 1
allow-blank: true
label: $y= $
suffix: $\rm{m}$
part2:
type: number-input
pl-customizations:
rtol: 0.05
weight: 1
allow-blank: true
label: $t= $
suffix: $\rm{s}$
part3:
type: number-input
pl-customizations:
rtol: 0.05
weight: 4
allow-blank: true
label: $x= $
suffix: $\rm{m}$
myst:
substitutions:
params:
vars:
title: Midair Propulsion
time_units: s
dist_units: m
velo_units: m/s
acc_units: m/s^2
v: 10
theta: 31
N: 3
C: 6.0
---
# Midair Propulsion
We launch a projectile at an angle $\theta = {{ params.theta }}^{\circ}$ in degrees and speed $v_0 = {{ params.v }}\ \rm{m/s}$ in a flat plane. At the peak of the projectile motion, a rocket turns on and starts accelerating the projectile in the $x$-axis according to the function $ a(t) = {{ params.C }} \times t^{ {{ params.N }} } $ in $\rm{m/s^2}$, where t is the time since the rocket turned on. Find the range it travels over the flight duration.
## Part 1
What is the maximum height the projectile will reach in {{ params.vars.dist_units }}?
### Answer Section
Please enter in a numeric value in {{ params.vars.dist_units }}.
## Part 2
How long will it take the projectile to reach this height in {{ params.vars.time_units }}?
### Answer Section
Please enter in a numeric value in {{ params.vars.time_units }}.
## Part 3
What is the range of travel for the projectile in {{ params.vars.dist_units }}?
### Answer Section
Please enter in a numeric value in {{ params.vars.dist_units }}.
## Attribution
Problem is licensed under the [CC-BY-NC-SA 4.0 license](https://creativecommons.org/licenses/by-nc-sa/4.0/).
