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

[dude24]

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!

 

[bob1182006]

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?

 

[dude24]

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?

 

[bob1182006]

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.

 

[dude24]

Can anyone else help me with the equations?

 

[Stevedye56]

What is 3^/circ meant to read as?

 

[bob1182006]

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?