Video: Using the Relative Velocity between Two Bodies Moving in a Straight Line to Find the Actual Speed of One of Them

A police car with a radar speed gun was moving on a highway at a speed of 48 km/h. A truck was moving toward it in the opposite direction. If the velocity of the truck relative to the police car was 169 km/h, determine the actual speed of the truck.

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Video Transcript

A police car with a radar speed gun was moving on a highway at a speed of 48 kilometers per hour. A truck was moving toward it in the opposite direction. If the velocity of the truck relative to the police car was 169 kilometers per hour, determine the actual speed of the truck.

Alright, so in this situation, we have a police car moving in one direction, as well as a truck moving toward the police car in the opposite direction. The officer in the car is equipped with a radar speed gun. This is a device that sends out a sound signal at a carefully calibrated speed which can then bounce off of moving objects and be reflected back to the police car. The total transit time for the signal indicates just how fast the moving object, in this case the truck, is traveling.

We’re told that relative to the police car, the truck was moving at 169 kilometers an hour. However, to a stationary observer watching the police car and the truck, this would not be the truck speed. That’s because the police car itself is in motion we’re told at a speed of 48 kilometers an hour. When our question asks about the actual speed of the truck. It’s talking about the speed of the truck relative to a stationary observer; that is one at rest with respect to the police car and the truck.

Now, an important clue in our problem statement is that the velocity of the truck relative to the police car is reported as a positive value. That means we can think of motion to the left as motion in the positive direction, and therefore, movement to the right is accounted negative. All this means that if we call the actual speed of the truck 𝑆 sub 𝐴, we’ll take the truck speed as perceived from the police car, positive 169 kilometers an hour. But then, we’ll subtract from this the police car speed itself.

Since we are talking about a speed and not a velocity, we use the value of positive 48 kilometers an hour. 169 minus 48 is 121. And this is the actual speed of the truck in kilometers per hour, or the speed of the truck relative to a stationary observer.

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