Calculating Distance: Jill's Sprint to Catch a Rolling Shopping Cart

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Homework Help Overview

The problem involves calculating the distance Jill has to run to catch a shopping cart rolling downhill from a hill tilted at 3 degrees. The context is kinematics, focusing on acceleration and motion under gravity.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss drawing diagrams to visualize the problem and determining the positions and accelerations of both Jill and the cart. Questions arise about the effects of the hill's angle on acceleration and the need to establish equations for their respective motions.

Discussion Status

Some participants have begun to outline the necessary equations to describe the motion of Jill and the cart. There is a request for further assistance in formulating these equations, indicating an ongoing exploration of the problem without a clear consensus yet.

Contextual Notes

Participants are considering the implications of the hill's angle on the cart's acceleration and are clarifying terms related to the problem setup. There is an emphasis on understanding the physical context before proceeding with calculations.

dude24
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Jill has just gotten out of her car in the grocery store parking lot. The parking lot is on a hill and is tilted 3^\circ. Fifty meters downhill from Jill, a little old lady let's go of a fully loaded shopping cart. The cart, with frictionless wheels, starts to roll straight downhill. Jill immediately starts to sprint after the cart with her top acceleration of 2.0 m/s^2.

How far has the cart rolled before Jill catches it?



I have no clue about how I should go about answering this problem!
 
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hm..K think i got it sorta.

first, draw a diagram, draw a line angle'd @ 3*. a point on the top will stand for Jill (I assume she's at the top of the hill o.o) and then 50m below that will be where the cart begins to roll down.

So determine your axe's. what is Jill's location? x=?
Also what acceleration does the cart have? What acceleration is acting on ALL bodies on Earth?

Also since they're at an angle of 3* will that affect their acceleration?
 
ok...so for the cart acceleration is g * sin (3) = .513
jill's location is at (0,0) and her acceleration shouldn't be factored in with the angle because her top acceleration given is 2 m/s^2 correct?
 
Edit: again to make it more readable.

Ok so you'll be working with acceleration's down the hill. the cart's acceleration is .513 m/s^2 down the hill. Jill's is 2.0m/s^2.

Now you need to determine when she will catch up to the cart.

So write out 2 equations that describe the location of the cart and Jill at time t.
 
Last edited:
Can anyone else help me with the equations?
 
What is 3^/circ meant to read as?
 
Stevedye56 said:
What is 3^/circ meant to read as?

he meant to say 3 and the little circle that represents degrees.

@dude24: write 2 equations that tell you where Jill is at time t. Do the same for the Cart at time t.

When you get those 2 how can you use them to determine at what time Jill catches the car?
 

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