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In this lesson, we will learn how to calculate displacements in vector component form and how to calculate the resultant displacement of multiple linear displacements.

Q1:

A cyclist rides 5.0 km east, then 10.0 km at an angle 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.

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:

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?

Q4:

A particle located initially at m undergoes a displacement of m. What is the final position of the particle?

Q5:

The 18th hole at Pebble Beach Golf Course is a dogleg to the left, with a length of 496.0 m. A golfer hits his tee shot a distance of 300.0 m, corresponding to a displacement Δ ⃑ 𝑟 = 3 0 0 . 0 ⃑ 𝑖 1 m , and hits his second shot 189.0 m with a displacement Δ ⃑ 𝑟 = ( 1 7 2 . 0 ⃑ 𝑖 + 8 0 . 3 ⃑ 𝑗 ) 2 m . What is the final displacement of the golf ball from the tee? Assume that the fairway off the tee corresponds to the positive 𝑥 -direction.

Q6:

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