Intro to Relative Velocity Practice Problems

Two circus artists ride two unicycles. The artist dressed in red has a velocity v_r = 1.5 î (m/s), and the one dressed in blue has a velocity v_b=-2.5 ĵ  (m/s). How fast does the artist dressed in blue appear to be moving compared to the artist dressed in red?

A "walkalator" is a walkway usually found in airports that are used to move people in longer distances for a shorter period of time, by either standing on it, or walking on it. In Changi Airport, the walkalators have lengths of 20 m and operates at a speed of 0.9 m/s. A boy runs starting on one end with a velocity of 2.9 m/s relative to the walkalator. How long will it take him to reach the opposite end if he runs in the opposite direction as the walkalator is moving?

A "walkalator" is a walkway usually found in airports that are used to move people in longer distances for a shorter period of time, by either standing on it, or walking on it. In Changi Airport, the walkalators have lengths of 20 m and operates at a speed of 0.9 m/s. A boy runs starting on one end with a velocity of 2.9 m/s relative to the walkalator. How long will it take him to reach the opposite end if he runs in the same direction as the walkalator is moving?

During filming for an action movie, Leo was running on top of a train that is moving due east at a speed of 16 m/s relative to the director who is standing on the side of the railtracks. What is the velocity of Leo relative to the train if Leo's velocity relative to the director standing on the side of the railtracks is 3.7 m/s due east?

The Lori River is a river that is known for its unusual width of 3 km. It flows towards north at a speed of 1.8 m/s. John tried riding their OppBoat, which is a boat that is used to cross the opposite sides of the river. The boat operator drives the OppBoat due west with a velocity of 7 m/s relative to the water. How much time is required for John to cross the opposite sides of the Lori River?

The Lori River is a river that is known for its unusual width of 3 km. It flows towards north at a speed of 1.8 m/s. John tried riding their OppBoat, which is a boat that is used to cross the opposite sides of the river. The boat operator drives the OppBoat due west with a velocity of 7 m/s relative to the water. What is John's velocity (magnitude and direction) relative to the earth? 

Mike is excited to try his boat which is given by his father as a gift on his birthday. The river is flowing 0.95 m/s west. As it is his first time driving a boat, he carefully drives the boat with a velocity of 0.30 m/s on the northwest direction. Calculate the velocity of the boat relative to the river.

Two residences, Ion Residences (located upstream) and Omega residences (located downstream) are located along a riverside. The distance between the two residences is 1800 m. Diego and Paul must make round trips between the two residences, starting from the Ion Residences. Paul is paddling a canoe at a constant speed of 4.50 km/h relative to the water in the river. On the other hand, Diego walks on the riverside at a constant speed of 3.7 km/h. The velocity of the river is 2.60 km/hr in the direction from Ion to Omega. How long will it take for Paul and Diego to make the round trip?

The pilot of a trainer plane wants to travel due east. A wind which is classified as "storm" by the weather station blows toward the north at a speed of 100 km/hr (approximately 62.1 mi/h). In what direction relative to the east-west line should the pilot travel if the airspeed of the plane (its speed in still air) is 300.0 km/h (about 186.4 mi/h)?

During an aviation training, the jet fighter is traveling due north. The pilot reads the ASI (airspeed indicator) as 70 m/s. Unfortunately, the weather is considerably harsh and the jet is subjected to a strong wind blowing toward the northeast direction at a speed of 27 m/s. Find the components of v_P/E if +x is considered as east and +y is north.

During aviation training, a jet fighter is traveling due north. The pilot reads the ASI (airspeed indicator) as 70 m/s. Unfortunately, the weather is considerably harsh and the jet is subjected to a strong wind blowing toward the northeast direction at a speed of 27 m/s. Which of the following vector-addition diagrams shows the correct relationship between v_J/E (jet velocity relative to the earth) and the two vectors?

A cyclist rides on a rainy day at a steady speed of 7 km/h along the x-axis in the positive direction. The cyclist remarks that the traces of the raindrops are tilted at an angle of 26 degrees clockwise from the vertical direction. Due to the bad weather conditions, she decides to make a U-turn. She moves now at the same steady speed along the x-axis in the negative direction. On her way back, she observes that the traces of the raindrop are now aligned with the vertical. Calculate the speed of the raindrops and their inclination with respect to a fixed frame on earth.

During an exhibition game, two jet skis start to move at the same time from the starting line. During the first minute, the two jet skis move at a constant velocity. The blue jet ski moves at a speed of 15.0 km/h north of east, while the red jet ski moves at a speed of 10.0 km/h in a direction of 30.0° west of north. Calculate the speed of the red jet ski with respect to the blue after 30.0 s of motion.

An athlete swims due east along a straight path of 200 m in the sea. The speed of the swimmer is constant and equal to 1.25 m/s with respect to the water. During the swim, the magnitude of the surface sea currents was 0.50 m/s, and their directions were due south. Calculate the time taken by the swimmer to finish the 200 m.

If a car travels northward at 60 mph while encountering a gusty wind from the northwest at an average speed of 20 mph, determine the car's velocity (magnitude and direction) relative to the ground.

A passenger on a moving train is walking towards the front of the train at a speed of 1.5 m/s. Simultaneously, the train is traveling forward at 20 m/s. i) Determine the passenger's velocity relative to the ground. ii) If the passenger walks towards the train's rear, find their velocity relative to the ground.

A boat is traveling eastward across a river with a speed of 40 mph relative to the water. Simultaneously, the river is flowing southward at a speed of 5 mph. If no corrective measures are taken, how much will the boat drift from its intended position over 18 minutes?

A helicopter is traveling westward at an airspeed of 125 km/h. A crosswind from the northeast begins to affect the helicopter, with an average velocity of 35 km/h. In what direction should the helicopter's nose be pointed to minimize lateral drift and maintain a westward course?

A swimmer can swim at a speed of 2.5 m/s in still water. When swimming across a river with a current, the swimmer must angle at 40° with respect to a line perpendicular to the shore to maintain a straight path as shown in the figure below. What is the swimmer's resultant speed with respect to the shore?

If a jetski can maintain a speed of 3.5 m/s in water with no water current and decides to traverse the river with a width of 80 m while encountering a water current at 1.2 m/s in a direction parallel to the riverbank, i) how far from a point directly across their starting position will they end up? ii) What is the time taken for them to reach the opposite side of the river?

An athlete is practicing rowing in a river that is 50.0 m wide. The river's current flows at 0.80 m/s. The athlete can row with a speed of 2.50 m/s relative to the water. If the athlete starts from one bank and rows directly across to the other side, determine the time it takes to reach the opposite bank and the distance downstream where the athlete lands, assuming the athlete initially aims to land directly opposite the starting point as shown.

Two aircraft are flying in the sky with paths that intersect at a right angle. Aircraft A is flying north at a speed relative to the Earth of $v_{Ae}=250\ \frac{km}{hr}$, and Aircraft B is flying east at $v_{Be}=320\ \frac{km}{hr}$. Calculate the relative velocity of Aircraft A as observed from Aircraft B. What is the velocity of Aircraft B relative to Aircraft A?

A kayaker can paddle at a speed of 2.0 m/s in still water. (i) If the kayaker wants to reach a point directly across a river with a width of 80 m and a current flowing at 1.5 m/s, at what angle upstream should the kayaker aim? (ii) How long will it take the kayaker to cross the river?

Raindrops appear to fall at an angle of θ with the vertical looking through a car window, which is moving at a speed v_c. What would the speed of the raindrops be in the reference frame of a stationary pedestrian outside of the car if she observes the raindrops falling vertically?