Question

A woman pushes a grocery cart filled with groceries up a hill with an 8.0° slope. She stops to rest a distance of 30.0 m up the hill and accidently lets go of the cart. The cart with its groceries has a mass of 18 kg. How long does it take for the cart to roll the distance of 30.0 m down the hill? Ignore friction.

1.6 s, 2.5 s, 6.6 s, or 9.8 s ?

How do I solve this? Thanks so much :)

Answer 1

this is physics.

Answer 2

yes:)

Answer 3

Have you learned formulas for distance? It looks like we need one that has mass in it.

Answer 4

sorry it's posted in the maths section! i can't gain access to the physics subject still :(

Answer 5

yes :) but I'm not sure which to use?

Answer 6

is it Fnet=ma ?

Answer 7

Have you seen v = a t
\[ s = 1/2 a t^2 \]

Answer 8

looks familiar but i forget how to use it!!

Answer 9

we need distance
we need a
then we solve for t

Answer 10

distance= 30
a=18 ?

Answer 11

I think a is g, but only the component in the direction parallel to the slope
g cos(82)

Answer 12

ohh so how do we sub everything into that equation? :O

Answer 13

apparently we do not need to know the mass (it might matter if we have friction)

Answer 14

a= g cos(82)
s= 30

Answer 15

ohh so 30=1/2(cos(82)(t)^2 ?

Answer 16

yes

Answer 17

and then 30=0.474838849(1/2(t^2))

63.1793293=1/2t^2 ?

Answer 18

oh, don't forget g= 9.8

Answer 19

oh! where do i put that in?

Answer 20

look up above: a= g cos(82)

Answer 21

ohh okay:)

so 30= 1/2(9.8*cos(82))(t)^2

30=4.65342072(1/2t^2)

6.44687034=1/2t^2

12.8937407=t^2

t=3.59

? :/ did i do that right? :/

Answer 22

oh wait oops

Answer 23

oh wait not sure where i went wrong :(

Answer 24

looks like radians instead of degrees

Answer 25

ohhh :(

i'm using google as my calculator right now because i left my calculator in my locker at school :( how can i make it degrees on google?

Answer 26

try cos(82 degrees)

Answer 27

okay:)

Answer 28

oh okay yay!! it worked!!

so like this then?
30/1.36389639=1/2t^2

21.9958057=1/2t^2
43.9916114=t^2

t=6.6326172

so 6.6 s ? :O

Answer 29

yes, that looks good.

Answer 30

yay!! thanks so much!!! :D will remember to put it on degrees when i use my actual calc!!