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Worksheet: Displacement Vectors

Q1:

A cyclist rides 5.0 km east, then 10.0 km at an angle 2 0 west of north. From this point she rides 8.0 km west. What is the final displacement from where the cyclist started? Consider east to correspond to positive horizontal displacement and north to correspond to positive vertical displacement.

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

Q2:

A pedestrian walks 6.00 km east and then 13.0 km north.

Find the pedestrian’s resultant displacement.

At what angle north of east does the pedestrian walk?

Q3:

In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind shifts a great deal during the day, causing the castaway to lose control of her raft. A search party used satellite images to track her movement from the point that she left the island. Meanwhile a rescue party traveled to intercept her. The following movements were tracked and relayed to the rescue party: 4 5 . 0 north of west for 2.50 km, then 6 0 . 0 south of east for 4.70 km, then 2 . 5 0 south of west for 5.10 km, then 5 . 0 0 east of north for 1.70 km, then 5 5 . 0 south of west for 7.20 km, and finally 1 0 . 0 north of east for 2.80 km. At this point the castaway was rescued.

What was the magnitude of the displacement of the castaway from the point she left the island to the point where she was rescued?

What was the direction of the castaway’s displacement from the point she left the island to the point where she was rescued?

Q4:

The F-35B is a short-takeoff and vertical landing fighter jet. An F-35B takes off vertically upward to a height of 20.00 m, while still facing horizontally. The fighter then follows a flight path that is angled at 3 0 . 0 0 above a line parallel to the ground, 20.00 m vertically above the ground. The fighter flies for a distance of 20.00 km along this trajectory. What is the fighter’s final displacement?

  • A 1 . 7 5 3 × 1 0 + 1 . 0 0 5 × 1 0 4 4 i j m
  • B 1 . 5 7 2 × 1 0 + 1 . 0 2 0 × 1 0 4 4 i j m
  • C 1 . 5 7 0 × 1 0 + 1 . 0 2 5 × 1 0 4 4 i j m
  • D 1 . 7 3 2 × 1 0 + 1 . 0 0 2 × 1 0 4 4 i j m
  • E 1 . 0 5 7 × 1 0 + 1 . 2 0 5 × 1 0 4 4 i j m

Q5:

An airplane is initially at a point 𝑃 1 . The airplane flies 32.0 km in a straight line, travelling 3 5 . 0 south of west, where it arrives at point 𝑃 2 . A helicopter also flies from 𝑃 1 to 𝑃 2 , but the helicopter initially travels in a direction 4 5 . 0 south of west, turning once to rotate its direction of travel by 9 0 . 0 .

Find the distance that the airplane would need to fly directly west from 𝑃 1 to have the same westward displacement as the westward displacement from 𝑃 1 to 𝑃 2 .

Find the distance that the airplane would need to fly directly south from 𝑃 1 to have the same southward displacement as the southward displacement from 𝑃 1 to 𝑃 2 .

Find the distance that the helicopter travels south of west.

Find the distance that the helicopter travels west of north.

Q6:

Aaron Rogers throws a football at 20.0 m/s to his wide receiver, who runs straight down the field at 9.40 m/s for 20.0 m. If Aaron throws the football when the wide receiver has reached 10.0 m, what angle does Aaron have to launch the ball so the receiver catches it at the 20.0 m mark?

Q7:

Suppose you walk 18.0 m straight west and then 25.0 m straight north.

What is the distance from your starting point to where you are now?

What is the compass direction of a line connecting your starting point to your final position?

Q8:

A trapper walks a 5.0-km straight-line distance from her cabin to the lake, as shown in the following figure.