In this worksheet, we will practice using vector operations to solve real-world problems on different topics, such as navigation and physics.

**Q1: **

A police car was moving along a horizontal highway at 47 km/h. It used a radar to measure the speed of a truck moving in the same direction. Given that the reading on the radar was 50 km/h, determine the actual speed of the truck.

**Q3: **

Two cars are moving on the same straight road with velocities of 87 km/h and 85 km/h, respectively. Given that is a unit vector in the direction of movement of the first car, determine the relative velocity of the first car relative to the second, given that both cars are moving in the same direction.

- A km/h
- B km/h
- C km/h
- D km/h

**Q4: **

Two cars and are moving in opposite directions on the same road at 62 km/h and 31 km/h, respectively. Given that is a unit vector in the direction of movement of car , determine the velocity of car relative to car .

- A km/h
- B km/h
- C km/h
- D km/h

**Q5: **

Two children are throwing a ball to each other straight across the back seat of a car, perpendicular to the direction of travel of the car. The ball is being thrown at 10 mph relative to the car, and the car is traveling in a straight line at 25 mph along the road. If one child misses the ball, letting it fly out of the window, find the angle it makes relative to the car’s forward direction ignoring wind resistance. Give your answer in degrees, correct to one decimal place if necessary.

**Q6: **

Two children are throwing a ball to each other straight across the back seat of a car, perpendicular to the direction of travel of the car. The ball is being thrown at 8 mph relative to the car, and the car is traveling in a straight line at 45 mph along the road. If one child misses the ball, letting it fly out of the window, find the angle it makes relative to the car’s forward direction ignoring wind resistance. Give your answer in degrees, correct to three decimal places if necessary.

**Q7: **

A man starts walking from home and walks 3 miles at north of west, then 5 miles at west of south, then 4 miles at north of east. If he walked in a straight line back home, how far would he have to walk and in what direction? Give your answers correct to three decimal places.

- A 9.762 miles, 7.623 north of west
- B 5.351 miles, 56.982 north of west
- C 5.351 miles, 56.983 west of north
- D 2.868 miles, 86.474 north of west
- E 2.868 miles, 86.474 west of north

**Q8: **

Find the values of , , and that make the two vectors and equal.

- A , ,
- B , ,
- C , or , or
- D , or , or

**Q9: **

Velocity is a vector quantity which combines speed and direction. For example, the velocity of a section of the Mississippi river near New Orleans is 3 miles per hour east.

What is the magnitude of this velocity?

What is the direction of this velocity?

- Aeast
- B 3 miles per hour east
- CNew Orleans
- DMississippi
- E miles per hour east

**Q10: **

Two cars are moving on the same straight road with velocities of 17 km/h and 50 km/h, respectively. Given that is a unit vector in the direction of movement of the first car, determine the relative velocity of the first car relative to the second, given that both cars are moving in the same direction.

- A km/h
- B km/h
- C km/h
- D km/h

**Q11: **

Two cars and are moving in opposite directions on the same road at 13 km/h and 82 km/h, respectively. Given that is a unit vector in the direction of movement of car , determine the velocity of car relative to car .

- A km/h
- B km/h
- C km/h
- D km/h

**Q12: **

A police car was moving along a horizontal highway at 38 km/h. It used a radar to measure the speed of a truck moving in the opposite direction. Given that the reading on the radar was 70 km/h, determine the actual speed of the truck.