Word problems on vectors - Vectors

Word problems on vectors

Lessons

Notes:

• Magnitude of a vector: $|| \vec{v}|| = \sqrt{v_x^2 + v_y^2}$

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.
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,
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.

Word problems on vectors

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AlgebraIntroduction to vectors

AlgebraMagnitude of a vector

AlgebraDirection angle of a vector

AlgebraScalar multiplication

AlgebraAdding and subtracting vectors in component form

AlgebraOperations on vectors in magnitude and direction form

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Introduction to vectors

Magnitude of a vector

Direction angle of a vector

Scalar multiplication

Adding and subtracting vectors in component form

Operations on vectors in magnitude and direction form

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Lessons

Notes:

• Magnitude of a vector: ∣∣v⃗∣∣=vx2+vy2|| \vec{v}|| = \sqrt{v_x^2 + v_y^2}∣∣v∣∣=vx2​+vy2​​

Intro Lesson

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.

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?

Word problems on vectors

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Algebra
Introduction to vectors

Algebra
Magnitude of a vector

Algebra
Direction angle of a vector

Algebra
Scalar multiplication

Algebra
Adding and subtracting vectors in component form

Algebra
Operations on vectors in magnitude and direction form

or

• Magnitude of a vector: $|| \vec{v}|| = \sqrt{v_x^2 + v_y^2}$

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.

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,

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.