# Vectors

**Parallelogram of vectors - relative velocity**

**Q1. **Find the resultant of two forces 25 N and 20 N with an angle of 60° between them.

What is the angle between the resultant and the first force?

**Q2. **Find the resultant of two velocities, 40 m/s and 30 m/s, with ah angle of 90° between them.

What is the angle between the resultant and the first velocity?

**Q3. **The resultant of two forces is 60 N. It acts at an angle of 30° to one of the forces, which has a magnitude of 45 N.

Find the magnitude of the second force.

**Q4.** Find the resultant of two forces (80 N and 40 N) acting at an angle of 120° to each other.

What is the angle between the resultant and the first force?

**Q5. **What is the actual course and speed of a ship which is heading due north at a speed of 12 km/h, across a tide running due west at 5.0 km/h?

**Q6. **Find the resultant force on a stone in a catapult, if each of the two elastics in the catapult has a tension of 25 N and the angle between the elastics is 40°.

**Q7. **The pilot of an aircraft wishes to fly due north, but a wind of 45 km/h is blowing from the west.

If the aircraft can fly at 200 km/h in still air, in what direction must the pilot steer?

**Q8.** Find the time it takes a motor-launch, which moves through the water at 10 km/h, to travel across a river at right angles to the current which flows at 6.0 km/h.

The width of the river
is 1.2 km.

**Q9. **Two cars leave a road junction at the same time.

Car A travels north at 45 km/h and car B travels east at 60 km/h.

Find the apparent speed and direction of B as seen by an observer in A.