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Vector arithmetic practice

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Wize University Physics Textbook (Master) > Introduction to Vectors

Vectors and Their Components

6 Activities

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Consider the vectors a⃗=−2i^+3j^−k^;   b⃗=4i^+3k^;   c⃗=−i^+3j^−k^\vec a=-2\hat i+3\hat j-\hat k; ~~~\vec b= 4\hat i+3\hat k; ~~~ \vec c=-\hat i+3\hat j-\hat k.

a) For each of these three vectors, find the magnitude.
b) For each of these three vectors, find a unit vector pointing in the same direction.
More Vectors and Their Components Questions:
Practice: Magnitude of a Vector
Practice: Magnitude of a Vector
An aircraft's location is 200 miles from base, at a direction of 30° W of S, at an altitude of 35,000 ft. Find the distance between the aircraft and the base.
Note: 1 mile = 5280 feet
I'm moving and packed all my books into a box that weighs 17kg. I pull the box on a weightless dolly with a force of 60N at an angle of 30° to the horizontal surface.
a) What is the acceleration of the box?
b) The box feels the normal force from the ground and the force of gravity. Are the normal force and gravity an action-reaction pair? Explain your answer!
Component vectors practice
You try to pull a heavy box by attaching a rope and pulling with a force of 20.0 N at an angle of 13.4 degrees above horizontal. What are the components of this force in the horizontal and vertical directions? Draw a diagram to support your answer.
A rabbit, escaping a fox, runs 40o north of west at 10.0m/s. A coordinate system is established with the positive x-axis to the east and the positive y-axis to the north. Write the rabbit’s velocity in terms of components and unit vectors.
Break into components
Given a velocity of 5.0m/s at 40.0o above the -x axis:
Which of the following is an example of a vector quantity?
Which of the following operations will not change a vector?
Practice Vector Components
Find horizontal and vertical components of a vector R shown in the Figure.
A bowling ball with mass of 1 kg travelling at 0.75 m/s hits a 0.5 kg bowling pin, initially at rest. The bowling pin moves off with a speed of 0.25 m/s at an angle of 35º relative to the initial direction of the bowling ball. What is the final velocity of the bowling ball? (note: you cannot assume kinetic energy is conserved).
Particle m1 with mass of 4×10−254 \times 10^{-25}kg is travelling with a velocity of 5msi^5\frac{m}s\hat i , and collides with particle m2 with mass 6×10−25 kg6\times 10^{-25}~\rm kg which is initially at rest. After the interaction, m1 travels with speed of 5 m/s at an angle of 45 degrees with vector.
What is the total momentum of the system?
What is the vector velocity of m2?