Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Velocity Vectors

Q1:

An athlete crosses a 30.0 m wide river by swimming perpendicular to the water current at a speed of 0.500 m/s relative to the water. He reaches the opposite side at a distance 75.0 m downstream from his starting point.

How fast is the water in the river flowing with respect to the ground?

What is the speed of the swimmer with respect to a friend at rest on the bank of the river?

Q2:

The velocity of the wind relative to the water is crucial to sailboats. Suppose a sailboat is in an ocean current that has a velocity of 2.20 m/s in a direction 3 0 . 0 east of north relative to Earth. It encounters a wind that has a velocity of 4.50 m/s in a direction of 5 0 . 0 south of west relative to Earth.

What is the speed of the wind relative to the water?

What is the direction of the wind, south of west, relative to the water?

Q3:

An airplane is flying through a jet stream that is blowing at 45.0 m/s in a direction 2 0 south of east. The direction of the plane’s motion relative to Earth is 4 5 . 0 south of west, while its direction of travel relative to the air is 5 . 0 0 south of west.

What is the airplane’s speed relative to the air mass?

What is the airplane’s speed relative to Earth?

Q4:

Bryan Allen pedaled a human-powered aircraft across the English Channel from the cliffs of Dover to Cap Gris-Nez on June 12, 1979. He flew for 182 min at an average velocity of 3.17 m/s relative to Earth in a direction 4 5 south of east.

What was the magnitude of his displacement in kilometers?

Allen encountered a headwind averaging 2.50 m/s almost precisely in the opposite direction of his motion relative to Earth. What was his average speed relative to the air?

What was the magnitude of his displacement relative to the air mass in kilometers?

  • A 48.9 km
  • B 34.6 km
  • C 61.9 km
  • D 27.3 km
  • E 55.4 km

Q5:

In the diagram, the two velocities v 𝐴 and v 𝐵 add to give the total velocity v t o t . For each part of the question, give the velocities in units of meters per second.

Find the magnitude of v 𝐴 .

Find the magnitude of v 𝐵 .

What is the 𝑥 -component of v t o t ?

What is the 𝑦 -component of v t o t ?

Consider that v t o t is rotated 4 0 clockwise about the origin. By how much does the magnitude of v t o t change?

Q6:

A boat leaves a dock at the time 𝑡 = 0 , heading out into a lake. The boat accelerates at 0 . 3 6 / m s i . A strong wind pushes the boat, giving it an additional velocity v i j = ( 1 . 4 + 1 . 1 ) m/s.

What is the net velocity of the boat at 𝑡 = 7 . 4 s?

  • A ( 2 . 1 + 2 . 1 ) i j m/s
  • B ( 1 . 1 + 4 . 1 ) i j m/s
  • C ( 4 . 1 1 . 1 ) i j m/s
  • D ( 4 . 1 + 1 . 1 ) i j m/s
  • E ( 1 . 1 1 . 1 ) i j m/s

What is the displacement relative to the dock of the boat at 𝑡 = 7 . 4 s?

  • A ( 2 0 + 8 . 1 ) i j m
  • B ( 1 5 + 7 . 1 ) i j m
  • C ( 1 1 + 4 . 6 ) i j m
  • D ( 6 . 5 + 3 . 2 ) i j m
  • E ( 2 2 + 9 . 4 ) i j m

Q7:

The velocity vector of a polar bear is v i j = ( 1 8 . 0 1 3 . 0 ) / k m h . Consider i and j to correspond to east and north, respectively.

What is the speed of the polar bear?

In what geographic direction is the bear heading?

Q8:

A convoy of vehicles has a velocity vector v i j k = ( 4 . 0 0 0 + 3 . 0 0 0 + 0 . 1 0 0 ) / k m h . What is the unit vector of the convoy’s direction of motion?

  • A ( 4 0 . 5 0 + 3 3 . 3 3 + 1 . 0 1 ) × 1 0 i j k 2
  • B ( 8 0 . 0 8 + 5 5 . 9 9 1 0 . 0 0 ) × 1 0 i j k 2
  • C ( 1 9 . 9 9 + 1 5 . 5 6 + 2 . 2 2 ) × 1 0 i j k 2
  • D ( 7 9 . 9 8 + 5 9 . 9 9 + 2 . 0 0 ) × 1 0 i j k 2
  • E ( 7 7 . 7 6 + 5 0 . 0 5 2 . 9 9 ) × 1 0 i j k 2

Q9:

Two motorboats piloted by Isabella and Jacob were moving on a lake. Their motion was recorded at different times. At 9:00, Isabella was moving north at 6 knots and Jacob was moving west at 6 knots. At 9:30, Isabella was moving west at 6 knots and Jacob was moving west at 3 knots. At 10:00, Isabella was moving northeast at 6 knots and Jacob was moving south at 3 knots. At 10:30, Isabella was moving northeast at 6 knots and Jacob was moving southwest at 6 knots. Finally, at 11:00, both were moving northeast at 2 knots but Jacob was moving closer to the shore.

At 9:00, were Isabella and Jacob’s velocity vectors equal to or unequal to each other?

  • Aunequal
  • Bequal

At 9:30, were Isabella and Jacob’s velocity vectors equal to or unequal to each other?

  • Aunequal
  • Bequal

At 10:00, were Isabella and Jacob’s velocity vectors equal to or unequal to each other?

  • Aequal
  • Bunequal

At 10:30, were Isabella and Jacob’s velocity vectors equal to or unequal to each other?

  • Aequal
  • Bunequal

At 11:00, were Isabella and Jacob’s velocity vectors equal to or unequal to each other?

  • Aequal
  • Bunequal

Q10:

A jet airplane flying from Darwin, Australia, has an airspeed of 260 m/s in a direction 5 . 0 south of west. It is in the jet stream, which is blowing at 35.0 m/s in a direction 1 5 south of east.

What is the speed of the airplane relative to Earth?

In what direction is the airplane traveling, south of west, relative to Earth?

Q11:

A drone’s average velocity vector v i j k = ( 1 5 . 0 + 3 1 . 7 + 2 . 5 0 ) / m s . What is the drone’s average speed?

Q12:

A Lockheed Martin F-35 II Lightning jet takes off from an aircraft carrier with a runway length of 95 m. The jet’s takeoff speed at the end of the runway is 0 . 8 0 × 1 0 2 m/s. At the point of leaving the deck of the aircraft carrier, the F-35’s acceleration decreases to a constant acceleration of 4.5 m/s2 at 2 7 above the horizontal.

What is the initial acceleration of the F-35 on the deck of the aircraft carrier to make it airborne?

At what altitude is the fighter 7.3 s after it leaves the deck of the aircraft carrier?

What is the velocity of the fighter 7.3 s after it leaves the deck of the aircraft carrier?

  • A ( 1 3 0 + 1 5 ) i j m/s
  • B ( 1 1 0 + 1 2 ) i j m/s
  • C ( 1 1 0 + 1 5 ) i j m/s
  • D ( 1 2 0 + 1 2 ) i j m/s
  • E ( 1 3 0 + 1 8 ) i j m/s

How far has the fighter traveled horizontally 7.3 s after it leaves the deck of the aircraft carrier?

Q13:

A ship sets sail from Portsmouth, England. The local ocean current is 2.50 m/s in a direction 3 0 south of west. If the ship is traveling at 8.00 m/s relative to the water, in what direction, east of south, would it have to travel in order to have a velocity straight south relative to Earth?

Q14:

A seagull flies at a velocity of 8.00 m/s straight into the wind. It takes the bird 24.0 min to travel 5.00 km relative to Earth.

What is the speed of the wind?

If the bird turns around and flies with the wind, how long, in minutes, will it take to return 5.00 km?

Q15:

A ship sets sail from Rotterdam, The Netherlands, heading due north at 8.00 m/s relative to the water. The local ocean current is 2.50 m/s in a direction 3 0 . 0 north of east. What is the speed of the ship relative to Earth?

Q16:

A ship sailing in the Gulf Stream is heading 2 5 . 0 west of north at a speed of 4.00 m/s relative to the water. Its velocity relative to Earth is 4.80 m/s, 5 . 0 0 west of north. What is the velocity of the Gulf Stream? (The velocity obtained is typical for the Gulf Stream, a few hundred kilometers off the east coast of the United States.)

  • A 1.43 m/s, 4 3 . 5 east of north
  • B 1.27 m/s, 4 2 . 3 north of east
  • C 1.98 m/s, 4 1 . 1 east of north
  • D 1.72 m/s, 4 2 . 3 north of east
  • E 1.10 m/s, 4 0 . 1 north of east

Q17:

A bird takes off and is carried by a strong wind. The bird travels straight northeast a distance of 95.0 km for 2.17 h before landing. Consider the 𝑥 -axis as due east and the 𝑦 -axis as due north.

What is the displacement from where the bird’s flight begins to where the it ends?

  • A ( 6 7 . 2 6 7 . 2 ) i j km
  • B ( 6 7 . 2 + 6 7 . 2 ) i j km
  • C ( 6 7 . 2 6 7 . 2 ) i j km
  • D ( 6 7 . 2 + 6 7 . 2 ) i j km
  • E ( 6 7 . 2 ) i km

What is the average velocity of the bird?

  • A ( 3 1 . 0 + 3 1 . 0 ) i j km/h
  • B ( 3 1 . 0 3 1 . 0 ) i j km/h
  • C ( 3 1 . 0 ) i km/h
  • D ( 3 1 . 0 + 3 1 . 0 ) i j km/h
  • E ( 3 1 . 0 ) i km/h

Q18:

A sandal is dropped from the top of an 18.0 m high mast on a ship moving at 3.05 m/s due south.

Calculate the velocity of the sandal relative to the ship when it hits the deck of the ship.

Calculate the velocity of the sandal relative to a stationary observer on the shore.

Q19:

The position of a particle for 𝑡 > 0 is given by r i j k ( 𝑡 ) = ( 3 . 0 𝑡 7 . 0 𝑡 5 . 0 𝑡 ) m

What is the particle’s velocity at 𝑡 = 2 . 0 s ?

  • A ( 2 1 7 2 + 1 . 0 ) i j k m/s
  • B ( 1 4 5 6 + 2 . 8 ) i j k m/s
  • C ( 1 0 6 6 1 . 3 ) i j k m/s
  • D ( 1 2 8 4 + 1 . 3 ) i j k m/s
  • E ( 9 . 8 7 1 + 3 . 1 ) i j k m/s

What is the particle’s speed at 𝑡 = 1 . 0 s ?

What is the particle’s speed at 𝑡 = 3 . 0 s ?

What is the average velocity of the particle between 𝑡 = 1 . 0 s and 𝑡 = 2 . 0 s ?

  • A ( 9 . 0 4 9 + 6 . 3 ) i j k m/s
  • B ( 8 . 8 5 2 + 9 . 3 ) i j k m/s
  • C ( 9 . 7 4 1 + 1 . 3 ) i j k m/s
  • D ( 9 . 5 4 2 + 2 . 3 ) i j k m/s
  • E ( 9 . 3 4 5 + 5 . 3 ) i j k m/s

Q20:

A small plane can fly at 175 km/h in still air. The plane flies in a wind that blows directly out of the west at 36 km/h.

At what angle west of north must the plane point in order for it to move directly north?

How much time is needed for the plane to reach a point 300 km directly north of its current position?