---
title: Jump Across Stream
topic: Kinematics(2D and 3D)
author: Jake Bobowski
source: Final 2016 Q4 P2
template_version: 1.3
attribution: standard
partialCredit: true
singleVariant: false
showCorrectAnswer: false
outcomes:
- 5.1.1.0
- 5.2.1.0
- 5.2.1.1
- 5.5.1.0
- 5.5.1.1
- 5.5.1.2
- 5.8.1.1
- 4.1.1.1
difficulty:
- medium
randomization:
- 2
taxonomy:
- undefined
span:
- chapter
length:
- long
tags:
- AK
- PW
assets: null
part1:
type: symbolic-input
pl-customizations:
label: $x = $
variables: t, g
weight: 1
allow-blank: false
part2:
type: symbolic-input
pl-customizations:
label: $y = $
variables: t, g
weight: 1
allow-blank: false
part3:
type: symbolic-input
pl-customizations:
label: $V_x = $
variables: t, g
weight: 1
allow-blank: false
part4:
type: symbolic-input
pl-customizations:
label: $V_y = $
variables: t, g
weight: 1
allow-blank: false
part5:
type: multiple-choice
pl-customizations:
weight: 1
part6:
type: number-input
pl-customizations:
rtol: 0.05
weight: 1
allow-blank: true
label: $x= $
suffix: $\rm{m}$
part7:
type: number-input
pl-customizations:
rtol: 0.05
weight: 1
allow-blank: true
label: $y= $
suffix: $\rm{m}$
part8:
type: symbolic-input
pl-customizations:
label: $\vec{V} = $
variables: i_hat, j_hat
weight: 1
allow-blank: false
part9:
type: multiple-choice
pl-customizations:
weight: 1
myst:
substitutions:
params:
vars:
title: Jump Across Stream
units: m
m: 243
w_s: 2
h_s: 1
v_i: 3
v_j: 4
h_b: 4
part5:
ans1:
value: Yes, the bear makes it to the other side of the stream.
ans2:
value: No, the bear does not make it to the other side of the stream.
part9:
ans1:
value: The problem would become a 1-D problem with motion only in the $y$-direction.
ans2:
value: The problem would become a 1-D problem with motion only in the $x$-direction.
---
# {{ params.vars.title }}
A very bored {{params.m}} $kg$ bear decided to jump across a stream.
The stream is {{params.w_s}} $m$ wide and the east bank of the stream is {{params.h_s}} $\rm{m}$ higher than the west bank (where the bear starts).
The bear can jump with an initial velocity $\overrightarrow{V_i} = $ {{params.v_i}}$\rm{m\over s}\hat{\imath}+$ {{params.v_j}} $\rm{m\over s}\hat{\jmath}$, and decides to start from {{params.h_b}} $\rm{m}$ in the air, halfway up a sturdy tree.
## Part 1
If the origin is at the bear's foot (up in the tree), write an equation describing the $x$ coordinate of the bear while it is in the air.
Use the following table as a reference. Note that it may not be necessary to use every variable.
| For | Use |
|----------|-------|
| $\Delta t$ | t |
| $g$ | g |
### Answer Section
## Part 2
If the origin is at the bear's foot (up in the tree), write an equation describing the $y$ coordinate of the bear while it is in the air.
Use the following table as a reference. Note that it may not be necessary to use every variable.
| For | Use |
|----------|-------|
| $\Delta t$ | t |
| $g$ | g |
### Answer Section
## Part 3
If the origin is at the bear's foot (up in the tree), write an equation describing the $V_x$ component of the velocity of the bear while it is in the air.
Use the following table as a reference. Note that it may not be necessary to use every variable.
| For | Use |
|----------|-------|
| $\Delta t$ | t |
| $g$ | g |
### Answer Section
## Part 4
If the origin is at the foot of the bear's jumping tree, write an equation describing the $V_y$ component of the velocity of the bear while it is in the air.
Use the following table as a reference. Note that it may not be necessary to use every variable.
| For | Use |
|----------|-------|
| $\Delta t$ | t |
| $g$ | g |
### Answer Section
## Part 5
Does the bear make it to the other side of the stream?
### Answer Section
- {{ params.part5.ans1.value}}
- {{ params.part5.ans2.value}}
## Part 6
When the bear is at its highest ($y$ or vertical) position above the stream, what is the $x$-coordinate of the bear?
### Answer Section
Please enter in a numeric value in {{ params.vars.units }}.
## Part 7
Where is the $y$-coordinate of the bear's highest position above the stream?
### Answer Section
Please enter in a numeric value in {{ params.vars.units }}.
## Part 8
What is the bear's velocity when it reaches its maximum height?
Use the following table as a reference.
| For | Use |
|----------|-------|
| $\hat{\imath}$ | i_hat |
| $\hat{\jmath}$ | j_hat |
### Answer Section
{{ substitutions.part8.label }}
## Part 9
This question is much easier to do in the frame of an observer moving with velocity $\vec{u} = $ {{params.v_i}} $\rm{m\over s}\hat{\imath} + $ 0 $\rm{m\over s}\hat{\jmath}$. Describe why?
### Answer Section
- {{ params.part9.ans1.value}}
- {{ params.part9.ans2.value}}
## Attribution
Problem is licensed under the [CC-BY-NC-SA 4.0 license](https://creativecommons.org/licenses/by-nc-sa/4.0/).

![The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.](https://raw.githubusercontent.com/firasm/bits/master/by-nc-sa.png)