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Worksheet: Relative Velocity

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

Q1:

A train 𝐴 of length 90 m was travelling at a speed of 170 km/h. It passed by another train 𝐡 of length 205 m. Find the time required for train 𝐴 to completely pass train 𝐡 , given that train 𝐡 is moving with a speed of 152 km/h in the same direction as train 𝐴 .

Q2:

A train 𝐴 of length 50 m was travelling at a speed of 116 km/h. It passed by another train 𝐡 of length 70 m. Find the time required for train 𝐴 to completely pass train 𝐡 , given that train 𝐡 is moving with a speed of 98 km/h in the same direction as train 𝐴 .

Q3:

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

  • A 𝑣 = 1 4 /  k m h , 𝑣 = 2 0 /  k m h
  • B 𝑣 = 5 6 /  k m h , 𝑣 = 2 0 /  k m h
  • C 𝑣 = 9 0 /  k m h , 𝑣 = 5 6 /  k m h
  • D 𝑣 = 5 6 /  k m h , 𝑣 = 9 0 /  k m h
  • E 𝑣 = 2 0 /  k m h , 𝑣 = 5 6 /  k m h

Q4:

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

Q5:

A ship was sailing with a uniform velocity directly towards a port that is 98 km away. A patrol aircraft passed over the ship travelling in the opposite direction at 410 km/h. When the aircraft measured the ship’s speed, it appeared to be travelling at 459 km/h. Determine the time required for the ship to reach the port.

Q6:

A police car moving in a straight line with a uniform velocity measured the relative velocity of a truck moving in the same direction to be 49 km/h. The police car then doubled its speed, measured the relative velocity again, and found that the truck appeared to be stationary. Find the real speeds of the police car 𝑣 c a r and the truck 𝑣 t r u c k .

  • A 𝑣 = 9 8 / c a r k m h , 𝑣 = 9 8 / t r u c k k m h
  • B 𝑣 = 9 8 / c a r k m h , 𝑣 = 4 9 / t r u c k k m h
  • C 𝑣 = 2 4 . 5 / c a r k m h , 𝑣 = 4 9 / t r u c k k m h
  • D 𝑣 = 4 9 / c a r k m h , 𝑣 = 9 8 / t r u c k k m h

Q7:

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

Q8:

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.

Q9:

A car is moving on a straight road at 102 km/h, and in the opposite direction, a motorbike is moving at 70 km/h. Suppose that the direction of the car is positive. Find the velocity of the motorbike relative to the car.

Q10:

A car 𝐴 was moving in a straight line at a uniform speed 𝑣 𝐴 . Another car 𝐡 was observed coming in the opposite direction with a relative speed of 86 km/h. When car 𝐴 doubled its speed, the relative speed became 138 km/h. If car 𝐡 was travelling with a uniform speed of 𝑣 𝐡 the whole time, find the actual speed of the two cars.

  • A 𝑣 = 1 0 4 / 𝐴 k m h , 𝑣 = 3 4 / 𝐡 k m h
  • B 𝑣 = 3 4 / 𝐴 k m h , 𝑣 = 5 2 / 𝐡 k m h
  • C 𝑣 = 5 2 / 𝐴 k m h , 𝑣 = 1 8 / 𝐡 k m h
  • D 𝑣 = 5 2 / 𝐴 k m h , 𝑣 = 3 4 / 𝐡 k m h

Q11:

A car 𝐴 was moving in a straight line at a uniform speed 𝑣 𝐴 . Another car 𝐡 was observed coming in the opposite direction with a relative speed of 79 km/h. When car 𝐴 doubled its speed, the relative speed became 119 km/h. If car 𝐡 was travelling with a uniform speed of 𝑣 𝐡 the whole time, find the actual speed of the two cars.

  • A 𝑣 = 8 0 / 𝐴 k m h , 𝑣 = 3 9 / 𝐡 k m h
  • B 𝑣 = 3 9 / 𝐴 k m h , 𝑣 = 4 0 / 𝐡 k m h
  • C 𝑣 = 6 6 / 𝐴 k m h , 𝑣 = 1 3 / 𝐡 k m h
  • D 𝑣 = 4 0 / 𝐴 k m h , 𝑣 = 3 9 / 𝐡 k m h

Q12:

A train 𝐴 travelling at 165 km/h passed another train 𝐡 that was travelling at 75 km/h in the same direction. Given that the length of train 𝐡 was 210 m and that it took 24 seconds for train 𝐴 to completely pass 𝐡 , find its length 𝐿 and the time 𝑑 it would take it to cross a bridge of length 105 m.

  • A 𝐿 = 8 9 0 m , 𝑑 = 2 . 2 9 s
  • B 𝐿 = 3 9 0 m , 𝑑 = 2 . 2 9 s
  • C 𝐿 = 8 9 0 m , 𝑑 = 1 0 . 8 s
  • D 𝐿 = 3 9 0 m , 𝑑 = 1 0 . 8 s

Q13:

Two cars 𝐴 and 𝐡 are moving at 142 km/h and 19 km/h in opposite directions. Given that car 𝐴 is moving in the positive direction, determine its relative velocity with respect to 𝐡 .

Q14:

A police car 𝐴 moving on a straight road at 71 km/h took notice of another car 𝐡 and a bicycle 𝐢 moving on the same road. Car 𝐡 was coming from the opposite direction and appeared to be traveling at a relative speed of 181 km/h, whereas the bicycle appeared to be moving backward at a relative speed of 37 km/h. Find the actual speeds 𝑣 𝐡 of car 𝐡 and 𝑣 𝐢 of bicycle 𝐢 .

  • A 𝑣 = 2 5 2 / 𝐡 k m h , 𝑣 = 3 4 / 𝐢 k m h
  • B 𝑣 = 1 1 0 / 𝐡 k m h , 𝑣 = 1 0 8 / 𝐢 k m h
  • C 𝑣 = 2 5 2 / 𝐡 k m h , 𝑣 = 1 0 8 / 𝐢 k m h
  • D 𝑣 = 1 1 0 / 𝐡 k m h , 𝑣 = 3 4 / 𝐢 k m h

Q15:

Two cars were moving in a straight line in opposite directions. Given that the distance between them was 17 km, the speed of one of the cars was 45 km/h, and the cars would meet after 5 minutes, determine the speed of the other car.

Q16:

Two warships were moving towards each other in the same straight line at 50 km/h and 89 km/h respectively. One of the ships fired a shell towards the other when the distance to it was 4.2 km. Given that the shell’s horizontal velocity relative to the first ship was 211 km/h, how long did it take for the the shell to hit the second ship?

Q17:

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 helicopters 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.

  • A 409 m
  • B 819 m
  • C 182 m
  • D 273 m

Q18:

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

Q19:

A person was riding a bicycle on a straight road at 14 km/h. If another person was also riding a bicycle in the same direction at 9 km/h, find the velocity of the second person with respect to the first.

Q20:

A car 𝐴 moving in a straight line measured the relative velocity of another car 𝐡 and found it to be 215 km/h in the opposite direction. After car 𝐴 reduced its speed to 0.65 of its previous value, the relative velocity of car 𝐡 became 180 km/h. Find the actual speed of both cars 𝑣 𝐴 and 𝑣 𝐡 .

  • A 𝑣 = 5 3 . 8 5 / 𝐴 k m h , 𝑣 = 1 6 1 . 1 5 / 𝐡 k m h
  • B 𝑣 = 1 0 0 / 𝐴 k m h , 𝑣 = 3 1 5 / 𝐡 k m h
  • C 𝑣 = 5 3 . 8 5 / 𝐴 k m h , 𝑣 = 2 6 8 . 8 5 / 𝐡 k m h
  • D 𝑣 = 1 0 0 / 𝐴 k m h , 𝑣 = 1 1 5 / 𝐡 k m h

Q21:

A police car with a radar speed gun was moving on a highway at a speed of 48 km/h. A truck was moving towards 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.

Q22:

A car, traveling at 16 km/h, and a motorcycle, traveling at 71 km/h, were moving on a straight road in the same direction. Given that n is the unit vector in the direction of the car, find the velocity of the motorcycle relative to the car.

  • A 8 7 n km/h
  • B βˆ’ 5 5 n km/h
  • C βˆ’ 8 7 n km/h
  • D 5 5 n km/h

Q23:

A police car moving on a straight road saw a motorcycle moving in the opposite direction. It appeared to be moving at 50 km/h. At the same time, the police car saw a truck that was moving in the same direction. It appeared to be moving at 76 km/h. Determine the speed of the truck relative to the motorcycle and its direction relative to the police car.

  • A 26 km/h, in the same direction of the police car
  • B 126 km/h, in the opposite direction of the police car
  • C 26 km/h, in the opposite direction of the police car
  • D 126 km/h, in the same direction of the police car

Q24:

A police car moving on a straight road saw a motorcycle moving in the opposite direction. It appeared to be moving at 121 km/h. At the same time, the police car saw a truck that was moving in the same direction. It appeared to be moving at 61 km/h. Determine the speed of the truck relative to the motorcycle and its direction relative to the police car.

  • A 60 km/h, in the same direction of the police car
  • B 182 km/h, in the opposite direction of the police car
  • C 60 km/h, in the opposite direction of the police car
  • D 182 km/h, in the same direction of the police car

Q25:

A police car moving on a straight road saw a motorcycle moving in the opposite direction. It appeared to be moving at 159 km/h. At the same time, the police car saw a truck that was moving in the same direction. It appeared to be moving at 48 km/h. Determine the speed of the truck relative to the motorcycle and its direction relative to the police car.

  • A 111 km/h, in the same direction of the police car
  • B 207 km/h, in the opposite direction of the police car
  • C 111 km/h, in the opposite direction of the police car
  • D 207 km/h, in the same direction of the police car

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