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Lesson: Using Vectors to Solve Problems

Worksheet: Using Vectors to Solve Problems • 12 Questions


A body moved 28 m due east and then 14 m due north. Determine the body’s displacement, stating its direction to the nearest minute.

  • A m, north of east
  • B m, north of east
  • C m, north of east
  • D m, north of east


A boat leaves the marina and sails 6 miles north, then 2 miles northeast. How many miles from the marina is the boat, and in what direction must it sail to head directly back to the marina? Give your answers correct to one decimal place.

  • A7.5 miles, south of west
  • B7.0 miles, south of west
  • C7.5 miles, west of south
  • D7.0 miles, west of south
  • E57.0 miles, south of west


A woman started walking from home and walked 6 miles at north of east, then 2 miles at east of south, then 5 miles at south of west. If she walked straight home, how far would she have to walk and in what direction? Give the distance in miles correct to 2 decimal places and the direction in degrees correct to one decimal place.

  • A1.93 miles, west of north
  • B6.06 miles, west of north
  • C0.97 miles, north of west
  • D1.93 miles, east of north
  • E6.06 miles, north of west


A woman leaves home and walks 3 miles west and then 2 miles southwest. How far from home is she? In what direction must she walk to directly head home? Give the distance, in miles, correct to two decimal places and the direction, in degrees, to one decimal place.

  • A4.64 miles, east of north
  • B4.15 miles, north of east
  • C4.64 miles, north of east
  • D4.15 miles, north of east
  • E21.50 miles, north of east


A plane is heading north with an airspeed of 500 km/h. However, there is a wind blowing from the southeast towards northwest at 50 km/h. How many degrees off course will the plane end up flying? What is the plane’s speed relative to the ground? Give your answers correct to one decimal place.

  • A, 550.0 km/h
  • B, 552.3 km/h
  • C, 536.5 km/h
  • D, 552.3 km/h
  • E, 536.5 km/h