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A rabbit, escaping a fox, runs 40o north of west at 10.0m/s. A coordinate syste…

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Wize University Physics Textbook (Master) > Introduction to Vectors

Vectors and Their Components

6 Activities

Wize University Physics Textbook (Master) > Motion in 1/2/3D: Kinematics

Basic Concepts of Kinematics

5 Activities

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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.

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!
Vector arithmetic practice
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.
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.
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?
More Basic Concepts of Kinematics Questions:
If you walked 3.00km West, and then 5.00km South to get to the store, what angle are you traveling at relative to the South direction? What is the magnitude of your displacement?
If you walked 3.00km West, and then 5.00km South to get to the store, what angle are you traveling at relative to the South direction? What is the magnitude of your displacement?
Practice question: position, velocity, and acceleration
The position of a particle is given by
r⃗(t)=(10t+t2+7)m\vec{r}(t)=(10t+t^2+7)m
a) Calculate instantaneous velocity at t =5 sec
Practice question: position, velocity, and acceleration
The position of a particle is given by
r⃗(t)=10t+t2+7\vec{r}(t)=10t+t^2+7
Calculate instantaneous velocity at t =5 sec, average velocity for interval (3-5 sec). Also calculate instantaneous acceleration at t =1 sec.
Forces: Friction
A professional mover drags a 20kg mattress across the floor. The mover exerts a force of 50 N at 30° to the horizontal. The coefficient of kinetic friction is 0.100. What is the acceleration of the mattress?
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!
Practice: Distance and Displacement
You drive 200 kilometres west to get from Montreal to Ottawa. On the way back to Montreal, you run out of gas after driving 50 kilometres.
Two runners (Bob and Alice) are racing. Alice is much faster than Bob and is placed such that she starts 25 m25\ mbehind Bob. She is 1.51.5times faster than Bob who runs at 8 m/s8\ m/s.
a) If they both start at the same time, when are these runners at the same point on the track?
b) Who will win in a 1000 m1000\ mrace if Alice has to start 200 m200\ mbehind? Explain your answer.
Throwing a rock down a well
Joe throws a rock straight down a well. He throws it at 13.0m/s, and the well is 5.10m deep. What is the velocity of the rock when it gets to the bottom? Use the conventional coordinates, where up is positive.
Franklin is coming over to your house. He first travels at 3m/s East, and then he travels 3m/s South. What direction is his average acceleration?
In horse racing, units of "horses" are used to measure length. It is defined as the length of a horse, or 8ft. And there are 3.28ft in 1m.
In the 1973 Belmont race, the horse Secretariat (great movie) won by 31 horse lengths. What is that distance in cm?
Riding a ferris wheel
Joanne is riding a ferris wheel that is 100.0m in diametre. Starting at the bottom, she rides 2 and 3/4 revolutions before the wheel gets stuck.
If you walked 3.00km West, and then 5.00km South to get to the store, what angle are you traveling at relative to the South direction? What is the magnitude of your displacement?
Taron is off on a rocket. He starts off at Earth, and launches off at 9am. He flies up 200km by 10am, and then another 150km by noon. He returns to Earth at 1:30pm. Give all answers in SI units.
(NB: the video says the trip ends at 2:30pm, this is incorrect. Should be 1:30pm, and the mathematics is still fine.)
a) What was his average speed for the whole trip?
Vanessa is making her way downtown, moving quite fast. She's racing Adam who's in a big yellow taxi. Their velocities are shown below
Over the entire race, who travelled the longest distance? Who has the greater displacement?
Average acceleration of runner
Frank is running at 3.0m/s. He accelerates until he is travelling at -1.3m/s. What is his average acceleration if it took him 12.0s to do this?
A bird flew 100m to the east then 200m to the northwest. Use the algebraic addition of vectors to find the bird’s net displacement.
A 20.0kg cart is moving at 10.0m/s before it goes down a hill. It ends up 2.0m below where it started, and travelled a distance of 15.0m. What is the speed of the car? There is friction, and it applies an average force of 2.00N over the course of it's motion.
Give your answer in m/s.
I over-packed a box and it weighs 50kg. I'm pulling it across a rough surface at an angle of 45 degrees above the horizontal with a force of 280N. The coefficient of kinetic friction of the floor is 0.5. I pull for 10 seconds, the box speeds up from rest, I release it and it continues to slide to a halt. What is its maximum speed?
Area under plot for displacement
Alice and Bob are having a race. Alice starts off strong, at 10.0m/s, while Bob struggles at 5.0m/s. But 5 minutes later, Alice starts to tire out, and slows to 2.0m/s. Bob sees his chance, and starts running at 7.0m/s. The race ends another 5 minutes later. Who travelled the furthest, winning the race?
Direction of acceleration
Joe is running from 20m to 10m, while he is slowing down. What direction is his acceleration?
If you walk around a circle of diameter of 10 m for π rad, how far have you walked?
Enter answer in meters.
Kinematics question
The slope of position-time graph gives
average velocity
Practice question: position, velocity, and acceleration
The position of a particle is given by
r⃗(t)=10t+t2+7\vec{r}(t)=10t+t^2+7
Calculate instantaneous velocity at t =5 sec, average velocity for interval (3-5 sec). Also calculate instantaneous acceleration at t =1 sec.
A 200g mass block is released from rest at a height of 25 cm on 30o incline. The incline is frictionless. It slides down the incline and then a frictionless surface until it collides elastically with an 800g block at rest 1.4 m from the bottom of the incline as shown in the figure. How much later do the two blocks collide again?
If the velocity of particle is non-zero. Can acceleration of particle be zero?
If the average velocity of an object is zero in some time interval, object's displacement is
zero
The position of a particle of mass 2g is given by r⃗=−3t2i^+2tj^+5k^\vec{r} = -3t^2\hat{i}+2t\hat{j}+5\hat{k} (t is in sec and r is in m).
The magnitude of instantaneous velocity and the magnitude of instantaneous acceleration at t = 3s are:
Practice question: position, velocity, and acceleration
The position of a particle is given by r⃗(t)=(10t+t2+7)m\vec{r}(t)=(10t+t^2+7)m
a) Calculate instantaneous velocity at t =5 sec
b) Calculate the average velocity for an interval (3-5 sec).