Physics 174 Fall 2022 Homework 02
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Physics 174
Fall 2022
Homework 02
1. Constant acceleration. Portals and Projectile Motion, created by UTA Eli Ullman-Kissel.
One of my favorite video games is Portal. It is a puzzle game where you can shoot an orange portal and a blue portal. These two portals connect to each other, and when you enter one, you exit the other with the same velocity you had, just shifted in the direction of the new portal. For example, if both portals were on the floor and you jumped into the orange one, you would exit the blue one with a velocity upwards. This is probably best understood by watching the trailer for the game:
Now, suppose we’ve put the blue portal on the ground on Earth, and the orange portal on the ground on the moon. Let the Earth’s gravity be gE = 9.81m/s2 and the moon’s gravity be gM = 1.625m/s2 . Now, imagine I jump (in 1D) into the blue portal from a diving board.
Let’s suppose you can survive about 16 seconds without breathing.
。Using the given info, what is the greatest height above the surface of the Earth I could jump so
that I spend less than 16 seconds on the Moon? (Assume that the differences in pressure/air/other factors are irrelevant.)
。What will my maximum distance above surface of the moon be?
It will help you to name the variables. So let’s call the exit velocity on Earth, which is the same as the entrance velocity on Moon, as v0 . Let’s call the quantities on Earth with subscripts: xe , te , and ge , for height, time, and gravitational acceleration, respectively. Similarly, the quantitites on the Moon will be xm , tm , and gm . The baseball example in the text may help.
2. Velocity profile. The total elevation gain was about 2200m and he finished in 4.5 hours. His max- imum speed during the ride was 60km/h. Here is what it roughly looks like as a function of time.
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。Draw the speed and acceleration. Assume initial conditions are zero. Draw the zero axis.
。Describe in words what is going on in terms of position, speed, and acceleration. For example,
you can say it’s moving forward until t1 , then backwards until t2 , etc.
3. Vectors. Suppose we have the coordinates for the start point and end point of two vectors A- and 
: For A-, the (x, y, z) values for start are (5, 1, 2) and for end are (10, 0, 3). For 
, the (x, y, z) values for start are ( ·3, ·2, 2) and for end are (1, 7, 4).
。Write each vector and find their magnitudes.
。Find the dot and cross products of the two vectors.
。Find the angle between the two vectors in degrees.
Suggested fun activity of the week.
。Read why mpg is confusing.
Why We Should Measure by Gallons per Mile, Not Miles per Gallon
https://www.popularmechanics.com/cars/a12367/4324986/
Time to Stop Measuring Fuel Economy in MPG?
https://www.smithsonianmag.com/science-nature/time-to-stop-measuring-fuel-economy-in-mpg-34304245
。Watch Mark Rober’s Measure height with a watch! Cliff jump science
and debunk someone’s claim about the height they jumped. If you do, tell us in Discussions on Canvas. That’s all!
2022-09-14