# Worksheet: Resultant Motion and Force

In this worksheet, we will practice representing motion in directions that are at right angles to each other as motion in one direction.

**Q1: **

A length of road stretches north for 10 km from the edge of a town to where it intersects an eastward road. A car is broken down on the eastward road, and the displacement of the edge of the town from the car has a magnitude of 24 km. How far east of the intersection is the car, to the nearest kilometer?

**Q2: **

Point is located 8 m horizontally from the base of the wall of a house, and point is located 6 m vertically above the base of the wall, as shown in the diagram. What is the magnitude of the displacement from point to point ?

**Q3: **

Two ropes tied around a heavy stone are pulled with the magnitudes and at the angles shown in the diagram. The 90 N force acts at an angle above the horizontal.

What is the magnitude of the net horizontal force acting on the stone due to the pull from the ropes? Answer to the nearest newton.

What is the magnitude of the net vertical force acting on the stone due to the pull from the ropes? Answer to the nearest newton.

**Q4: **

The force is the resultant of the two force vectors shown in the diagram. What is the magnitude of to the nearest newton?

**Q6: **

An athlete runs once completely around the edge of a rectangular field. The east–west running sides of the field are 40 m long and the north–south running sides are 20 m long. The runner’s average speed is 8 m/s.

While the first runner runs, a second runner runs back and forth between opposite corners of the field and reaches the opposite corner to her starting point for the second time at the same moment that the first runner completes his run all around the field’s edges.

What was the second runner’s average speed? Answer to two decimal places.

While the second runner runs between two opposite corners of the field, what is her average speed parallel to the east–west running sides of the field? Answer to two decimal places.

While the second runner runs between two opposite corners of the field, what is her average speed parallel to the north–south running sides of the field? Answer to two decimal places.

**Q7: **

An aircraft is flying eastward, accelerating at 12 m/s^{2}. The aircraft is also descending vertically with an
acceleration of 9 m/s^{2}. Before
accelerating, the eastward velocity of the aircraft was
250 m/s and its vertical
speed was 10 m/s. What is the
speed of the aircraft after 10 seconds of acceleration? Answer to the nearest meter per second.

**Q8: **

A bird flies along a line that displaces it 450 m east and 350 m north of its starting point, as shown in the diagram. What angle must the bird turn toward the west to change direction and fly directly north? Give your answer to the nearest degree.

**Q9: **

A vacationer stays in a tent on a campsite that is part of a landscape, as shown in the diagram. Two paths run from the campsite, one of which runs east to some shops. A sign at the campsite says that the shops are 100 m distant and that the other path is 130 m long and leads to some ruins. The vacationer walks to the shops and sees a sign there that says a garage is located 230 m to the north. The garage is 320 m west of the nearest town to the campsite. What is the magnitude of the displacement from the ruins to the town, to the nearest meter?

**Q10: **

Two aircraft scramble from the same airfield, one climbing at an angle of from the ground and the other at from the ground, as shown in the diagram. When both aircraft are horizontally 2,500 m from the airfield, the aircraft that climbed at a less steep angle is vertically meters above the ground, and the aircraft that climbed more steeply is vertically meters above the ground.

How far vertically above is , to the nearest meter?

How much greater is the displacement from the airfield of the fast-climbing aircraft than the displacement from the airfield of the slow-climbing aircraft when the fast-climbing is meters above the ground? Answer to the nearest meter.

**Q11: **

A friction force of 4,790 N acts on a car that is being driven at constant speed along a hill that slopes at . The car is driven by a force of 6,750 N from its engine. The direction of the force from the car’s engine is considered the positive direction.

What gravitational force acts on the car in the direction of the slope of the hill?

What is the mass of the car, to the nearest kilogram?