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Exercise #2 for a man on a train

A man is walking in a passenger car of a train that is moving at 1 mile per hour toward the northeast (45 degrees). The man is walking in the opposite direction than the train is moving at 2.933 feet per second. (Thismeans that the angle for the man's velocity vector is 225 degrees.)

What is the man's velocity with reference to the ground?

Another vector diagram for a man on a train

Figure 6 shows another vector diagram for a man on a train. Once again, theunits for both velocity vectors must be the same. Therefore, the length of the velocity vector for the man is based on a conversion from 2.933 feet persecond to 2 miles per hour.

Figure 6 - Another vector diagram for a man on a train.

Missing image.

Make a new html file

Please copy the code from the previous exercise into a new html file, make the changes described below, and open the html file in your browser.

  • Change the value of vecTrainAng from 0 to 45.
  • Change the value of vecManAng from 0 to 225.

(Because of the small differences between this script and the previous script, I won't publish a copy of this new script here.)

Screen output

The text shown in Figure 7 should appear in your browser window when you open the file in your browser.

Figure 7 . Screen output for Exercise #2 for a man on a train.
Start Script Velocity magnitude = 1.00 miles/hourVelocity angle = 225.00 degrees End Script

Analysis of the results

The man and the train are still moving along the same straight line even though the angle is no longer 0. Therefore, the magnitudes of the two vectorsstill add algebraically. In this case, however, the man and the train are moving in opposite directions, so they are no longer additive.

The man has a greater velocity magnitude

The magnitude of the man's velocity in the direction of 225 degrees is greater than the magnitude of the train's velocity in the opposite directionof 45 degrees.

As you can see from Figure 7 , the man's velocity with reference to the ground is 1 mile per hour at an angle of 225 degrees. This means that an observer standing on theground at a point on a line perpendicular to the train would perceive the man to be moving to the left at 1 mile per hour (assuming that the train is moving to the right).

An exercise with three vectors in a plane

Now we are going to take a look at an exercise involving three vectors in a plane, which are not in a line.

An aircraft carrier is steaming east with a uniform velocity of 2 milesper hour relative to the ground beneath the ocean. A large platform on the deck is sliding northeast with a uniform velocity of 2 miles per hour relative to the ship. A man is walking north on the platform with auniform velocity of 2 miles per hour relative to the platform.

What is the velocity of the platform with reference to the ground below the ocean?

What is the velocity of the man with reference to the ground below the ocean?

Vector diagram for man on aircraft carrier

Figure 8 shows a vector diagram for the man on the aircraft carrier.

Figure 8 - Vector diagram for man on aircraft carrier.

Questions & Answers

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Source:  OpenStax, Game 2302 - mathematical applications for game development. OpenStax CNX. Jan 09, 2016 Download for free at https://legacy.cnx.org/content/col11450/1.33
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