Lesson Worksheet: Relative Velocity Mathematics

In this worksheet, we will practice calculating the relative velocity of a particle with respect to another and calculating the relative velocity vector.


Two cars 𝐴 and 𝐵 are moving with velocities 41 km/h and 32 km/h, respectively, in the same direction. Determine 𝑣.


A car is moving on a straight road at 84 km/h, and in the opposite direction, a motorbike is moving at 45 km/h. Suppose that the direction of the car is positive. Find the velocity of the motorbike relative to the car.


Fill in the blank: If vi=25 and vi=40, then vi=.

  • A15
  • B−15
  • C−65
  • D65


If ve=50 and ve=−15, then the relative velocity ve=.

  • A−35
  • B−65
  • C65
  • D35


During a race, two cars, 𝐴 and 𝐵, are moving in a straight line in the same direction. Car 𝐴 is chasing car 𝐵. Car 𝐴 moves with a uniform velocity 250 km/h and the driver of car 𝐵 sees that car 𝐴 seems to be moving toward him with velocity 180 km/h. What is the actual velocity of car 𝐵?


A submarine fires a torpedo at a target as part of a training exercise. The velocity of the submarine relative to the stationary target is represented by the vector u. The velocity of the torpedo relative to the submarine is represented by the vector v. What does the vector uv+ represent?

  • Athe velocity of the torpedo relative to the stationary target
  • Bthe velocity of the submarine relative to the torpedo
  • Cthe total distance the torpedo travels
  • Dthe speed of the submarine
  • Ethe speed of the torpedo


A ship was sailing with a uniform velocity directly toward a port that is 144 km away. A patrol aircraft passed over the ship traveling in the opposite direction at 366 km/h. When the aircraft measured the ship’s speed, it appeared to be traveling at 402 km/h. Determine the time required for the ship to reach the port.


A train 𝐴 of length 65 m was moving at 74 km/h when it passed another train 𝐵 of length 210 m traveling at 106 km/h in the other direction. How long did it take for train 𝐴 to completely pass train 𝐵?


Two cars 𝐴 and 𝐵 are moving in the same direction on a straight road, where the velocity of car 𝐵 relative to car 𝐴 is 34 km/h. If car 𝐴 slowed down to a quarter of its velocity, the velocity of car 𝐵 relative to car 𝐴 would be 76 km/h. Determine the actual speeds of the two cars 𝑣 and 𝑣.

  • A𝑣=56/kmh, 𝑣=90/kmh
  • B𝑣=90/kmh, 𝑣=56/kmh
  • C𝑣=56/kmh, 𝑣=20/kmh
  • D𝑣=20/kmh, 𝑣=56/kmh
  • E𝑣=14/kmh, 𝑣=20/kmh


A helicopter flew in a straight line at 234 km/h above a train moving in the same direction. It took the helicopter 21 seconds to travel the length of the train. Following this, the pilot halved the helicopter's speed. Given that it took the train 14 seconds to pass the helicopter traveling at this speed, find the length of the train in meters.

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