Net displacement problem with two triangles

[ikihi]

Homework Statement

A ball on a porch rolls 60 cm to the porch's edge, drops 40 cm, continues rolling on the grass, and eventually stops 80 cm from the porch's edge.

What is the magnitude of the ball's net displacement, in centimeters?


ball starts rolling here
\/
rolls 60cm->
#----------#
******** -
******** - <- ball goes down 40 cm
******** -
******** #-----------------# <---ball stops rolling here

.....ball rolls 80cm ^

Homework Equations

The length of both a and b are known for both triangles, then c, the hypotenuse, can
......... _________
be calculated as follows: c=√a^2+b^2.

The Attempt at a Solution

72 cm and 89 cm are the hypotenuse's of two different triangles.

The first triangle is 40 and 60; The hypotenuse is 72 cm. The second is 40 and 80: this one's hypotenuse is 89 cm. I need to find the magnitude of the ball's net displacement. This is where I'm confused. And have I done this problem correct up to this point or am I way off?

 

[voko]

Why do you care about a point in the middle?

 

[ikihi]

Why do you care about a point in the middle?

I don't know. I may be over thinking this problem

 

[voko]

For displacement, only the end points are important. Consider them.

 

[ikihi]

For displacement, only the end points are important. Consider them.

Well I would say that where the ball started is the first point and the end point is where the ball stopped on the lawn. And so the displacement would probably be a straight line from the start to finish.

 

[voko]

That is correct.

 

[ikihi]

That is correct.

Ok. I understand the concept then. I just don't understand how to get the solution.

 

[voko]

Why exactly can you not compute the displacement? You were able to compute displacements to/from some arbitrary middle points.

 

[ikihi]

Why exactly can you not compute the displacement? You were able to compute displacements to/from some arbitrary middle points.

I'm not sure.
Is it the displacement of the first triangle(72cm) + 80cm for the remaining length traveled on the x axis?

152 cm?

 

[voko]

Again. You can compute the displacement to some arbitrary middle point ("the first triangle"). What can't you just do it for the entire displacement in the exact same way?

 

[ikihi]

Again. You can compute the displacement to some arbitrary middle point ("the first triangle"). What can't you just do it for the entire displacement in the exact same way?

vector addition?

 

[ikihi]

Again. You can compute the displacement to some arbitrary middle point ("the first triangle"). What can't you just do it for the entire displacement in the exact same way?

I guess I don't know the correct formula.
Am I correct in thinking that the unknown displacement wouldn't be part of a right triangle, and so I can't use the Pythagorean theorem?

 

[voko]

Look at the end points of the displacement in the diagram in your post #1. Then look at the point at the intersection of the vertical line from the first point, and the horizontal line from the second point. What can you say about the triangle made of these three points?

 

[ikihi]

Look at the end points of the displacement in the diagram in your post #1. Then look at the point at the intersection of the vertical line from the first point, and the horizontal line from the second point. What can you say about the triangle made of these three points?

Oh okay thankyou. So we can add 60 +80. and that's 140. and the y-axis is 40. so the displacement is 145.6cm.

it has 2 sig figs so would it be: ≈145 or ≈146 or ≈145.60 ?

 

[voko]

Very well. You should round it to the nearest integer, because your input did not have any meaningful decimal figures. You have .6 - does that round toward 0, or toward 1?

 

[ikihi]

Very well. You should round it to the nearest integer, because your input did not have any meaningful decimal figures. You have .6 - does that round toward 0, or toward 1?

toward 1