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

Question

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)? Remember of the correct number of significant figures.

Answer 1

We want to split this up into x and y parts first to make everything a little bit more clear. First, how far did the ball roll horizontally? Does the vertical drop make any difference to the horizontal distance?

 

The ball first moves 60 cm (let's say to the right), then another 80 cm right. This is a total of 140 cm.

 

Now for the vertical motion, it only has one move, which is 40 cm down (a negative number if you think about 'up' as the positive direction.

 

We have a total of 140 cm to the right and 40 cm down. Those are perpendicular to each other, right?

 

The displacement is defined to be the final position - the initial position. The magnitude is the absolute value of this.

 

We have the legs of a right triangle now. How can we find the hypotenuse? How is the hypotenuse of this triangle related to the magnitude of the displacement?

 

We get the hypotenuse using the Pythagorean Theorem. This is also the magnitude of the displacement.

 

sqrt ( 140² + (-40)² ) = 145.6 cm

 

Now for significant figures...You are given lengths as 60 cm, 40 cm, and 80 cm. If those were given as you wrote them, each has only 1 sig fig, so our answer needs to have only 1 sig fig as well. How can we change 145.6 cm to have 1 sig fig?

 

We look at the digit after the first one (the 4) and see if it rounds up or down. 4 rounds down, which means we get a final answer of 100 cm.

 

I hope this helps and if you have any questions, please ask.

 

EDIT: I used the wrong drop distance, and now the correct displacement is in the solution.

With respect to the sig figs, are the numbers written as 60. cm , etc? With the decimal after the 0? If so, that means they all have 2 sig figs, which means that the answer is rounded using the third digit.

 

The third digit is a 5, which means we should look at the previous digit to determine if it is rounded up or down. The rule is that we round to an even number, so this time, it goes down to 140 cm.

 

Sorry about the confusion.