A tennis ball moves 16 meters northward, then 22 meters southward, then 12 meters northward, and finally 32 meters southward. Determine the magnitude of the distance the object traveled and the magnitude and direction of the displacement

The tennis ball had a displacement of 26 meters southward.

The distance traveled is 82 m

Explanation:

Distance and Displacement

A moving object constantly changes positions at defined periods of time. The total moved distance is the sum of each individual distance the object traveled. It can be written as:

dtotal=d1+d2+d3+...+dn

This sum is obtained independently of the direction the object moves.

The displacement only takes into consideration the initial and final points of the path defined by the object in its moving. The displacement, unlike distance, is a vectorial magnitude and can be even zero if the object starts and ends the movement at the same point.

The tennis ball makes the following moves:

16 meters northward

22 meters southward

12 meters northward

32 meters southward

The total distance traveled is the sum of all the individual distances:

dTotal = 16 + 22 + 12 + 32 = 82 m

The distance traveled is 82 m

Following each move, we can determine where the tennis ball ended up. Suppose it began at the origin and the northward direction is positive and the southward direction is negative.

Thus, the total displacement is:

Disp = +16 - 22 + 12 -32 = -26 m

The tennis ball had a displacement of 26 meters southward.

about 45° and at the middel