# Word problems on vectors

### Word problems on vectors

#### Lessons

• Magnitude of a vector: $|| \vec{v}|| = \sqrt{v_x^2 + v_y^2}$
• Introduction
Introduction to word problems on vectors

• 1.
Solving Force Using Vectors
A 2000 lb car is parked stationary on a slope. The brake is applying a 600 lb force to keep it from sliding down. Determine the inclination of the slope.

• 2.
Finding Displacement Using Vectors
Kevin brings his dog to a park. He throws two balls for his dog to catch. The path of the first ball is described by the vector $v_1=130i+10j$ and that of the second ball is described by the vector $v_2=80i+(-40)j$ where the distances are all expressed in meters.
a)
How much farther did the first ball travel compared with the second ball?

b)
What is the distance between the two balls thrown?

• 3.
Evaluating Velocity Using Vectors
Elaine can swim in still water (no current) with a speed of 5 m/s. She now goes swimming in a river which has a current flowing towards west with a speed of 2 m/s. Assuming her speed is the same,
a)
What is her resultant velocity if she tries to swim due west along the current?

b)
What is her resultant velocity if she tries to swim due east against the current?

c)
What is her resultant velocity if she tries to swim north across the river? What would her resultant direction of travel be?

• 4.
Determining Displacement and Velocity Using Vectors
A plane is travelling south with a speed of 140 km/h. Simultaneously, there is a steady wind blowing due west with a speed of 40 km/h.
a)
Make a sketch illustrating the resultant velocity of the plane.

b)
What is the resultant speed of the plane?

c)
After 13 hours, how far away is the plane from its starting point?