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1. Distinguish the difference between a vector quantity and scalar quantity.
What does the length of a vector arrow represent?
Draw two displacement vectors: -5.0 meters and + 10 meters, making sure their lengths properly represent the difference between them.
2. What are the two rules for adding vectors? 1.
2.
How do you make subtracting vectors the same as adding vectors?
You can move vectors anywhere you want to on the page as long as you keep two things constant: a.
b.
A person walks north 10 meters and then rests. The person then walks north another 20 meters. If the trip took 20 minutes, find the person's final displacement average speed and average velocity. Show the vector diagram and the result of adding the two vectors. (disp = 30.0 meters North; avg speed = .025 m/s; avg vel = .025 m/s N).
What is the only difference between the average speed and average velocity in the last level?
A car drives 35.0 miles north and then 25.0 miles west in 1.0 hours. Find the displacement, average velocity and average speed of the car. Draw the vector diagram. (disp = 43 mph 35.5 deg W of N; avg vel = 43 mph 35.5 deg W of N; avg speed = 60 mph)
A car drives 65.0 miles south and then 70.0 miles east in 2.0 hours. Find the displacement, average velocity and average speed of the car. Draw the vector diagram. (disp = 95.5 miles 47.1 deg E of S; avg vel = 47.8 mph 47.1 deg E of S; avg speed = 67.5 mph)
Explain why the average speed and average velocity are not the same in the last two levels, when they are in level three.
3. A boat is heading up stream at 2.0 m/s, but the current is in the exact opposite direction at 3.0 m/s. Draw the vector diagram and find the boat's actual velocity. (-1.0 m/s if you consider up stream to be positive).
A small airplane is traveling West at 100 m/s, but there is a strong wind blowing from the North (North to South) at 30 m/s. Find the plane's resultant velocity and include the vector diagram. (104 m/s 17 degrees South of West).
A women starts walking from the lobby entrance 100 feet to the elevator. she takes the elevator to the 3rd floor, which is 200 feet above the lobby floor. Find her total displacement the moment she steps off of the elevator, and show the vector diagram. (224 ft 63 degrees above the lobby floor).
The total displacement of a jogger is 130 meters. If the jogger ran 120 meters down the street, how far did she run after she turned the corner? Include the vector diagram (50 meters).
After resting, the jogger continued home and ended up with a total displacement (from where she rested: this is a new problem) that made an angle of 53.13 degrees EoN (She started running north for a certain distance, and then turned and ran East for a certain distance). If the North leg of her trip was 30 meters, find her total displacement. Include a vector diagram. (50 meters).
4. If you are given vectors to add that have both an x and y component, what steps do you have to take in order to find the resultant?
Step Two:
Step Three:
A car drives 30 miles 40 deg W of N, then travels 100 miles 40 deg W of S. Find the car's final displacement. Include the vector diagram. (disp = 99 miles 57 deg W of S).
Would the car's average velocity and average speed be the same? Why or why not?
A person walks north 20 meters, then heads 50 meters 30 deg N of E, then turns and heads 100 meters West, and finally heads another 20 meters 50 degrees N of W. Find the average velocity if the trip took 20 minutes. Include the vector diagram. (avg Velocity = .077 m/s 41 deg N of W).
5. A boat is heading down stream with a velocity of 6.0 m/s 35 degrees W o S. The current is moving with a velocity of 5.0 m/s 25 deg S of E, and the wind is blowing straight East at 3.0 m/s. Find the actual velocity of the boat. Include a vector diagram. (vel = 8.1 m/s 60 deg S o E).
A biker rides 20 meters 40 degrees N of W, 30 meters 20 degrees N o W, 50 meters North, 100 meters East, 30 meters 30 degrees E o S, and finally another 30 meters 60 degrees W o S. What is the biker's final displacement? Include a vector diagram. (disp = 56 m 35 degrees N o E)
What is the biker's average speed for the trip if it took 20 seconds? (13 m/s)
What is the biker's average velocity for the trip if it took the same time? (2.8 m/s 35 degrees N o E).
6. Describe in your own words what the phrase "frame of reference" means and what it depends on:
An escalator is moving up at 1.0 m/s. If a person walks up the escalator with a speed of 2.0 m/s, how fast would that person be moving relative to someone at rest on the ground level? Show the vector diagram. (+ 3.0 m/s)
How fast would that person be moving relative to someone on the escalator who is at rest? (+ 2.0 m/s)
Why do the two people see two different speeds from the last two questions?
7. A car is traveling behind a truck at 30 mph. If the truck is traveling in the same direction as the car at 35 mph, what is the velocity of the car relative to the truck? Include the vector diagram. (V = -5 mph)
Would it look any differently to the truck if it was at rest and the car was traveling away from it at 5 mph? Explain.
Back to the original problem (car traveling at 30 and the truck at 35) what is the velocity of the truck as seen by the car? Include vector diagram. (+5 mph)
How do the two answers compare?
If a car traveling behind a truck, sees the truck moving in the negative direction, what must be true about the truck's velocity compared to the car's?
What direction would the truck see the car moving in that same situation?
What would have to be true about their velocities if they both saw each other as being at rest?
A car is heading south at 35 mph on a road that is under another road with a truck that is traveling East at 50 mph. Find the velocity of the car relative to the truck and the velocity of the truck relative to the car. Include the vectors. (Velocity of car relative to truck = 61 mph 55 deg W of S; Velocity of truck relative to car = 61 mph 35 deg N of E)
8. Which way would be the shortest way to cross a river in a boat: head straight across, or angle the boat so that it is going agaisnt the current which results in the boat heading straight across the river? Explain by using a vector diagram.
Which of the two ways above would take the least amount of time? Explain!
A boat is trying to cross a river. If the current of the river is 5.0 m/s, and the boat heads straight across, which is due east, with a speed of 5.0 m/s, find the boat's velocity relative to the shore. (7.1 m/s 45 deg SE).
Find how long it would take the boat to reach the other side of the river if the river's width was 100 meters. (20.0 seconds)
What direction should the boat head so that it actually travels straight across the river, if the river's current is now 3.0 m/s, and boat is now moving at 4.0 m/s? (49 degrees N of E)
How long will it take the boat to travel to the other side if it takes that angle? (37 seconds).
Why does it take more time for the boat to actually travel straight across (which is a smaller distance) compared to traveling down stream (Which is a longer distance)? (Don't just say because it is traveling faster. Explain why it is traveling faster!).
9. What are the two parts of motion for a projectile? 1.
2.
Why does the vertical component of velocity for a projectile change while the horizontal component stays constant? Assume no air-resistance.
A ball is rolling off of a roof of a house at 5.0 m/s. The house is 30 meters tall. How long will it take the ball to hit the ground? (2.5 seconds).
How far from the house will it drop? (x = 12.5 or 13 m)
What is the ball's velocity at 1.5 seconds? (v = 16 m/s 71 degrees BH).
What is the ball's final velocity? (v = 25 m/s 78 degrees BH).
From the last level: why is the final velocity so close to equaling the vertical component of the velocity?
Why are you able to use the vertical equations and horizontal equations separately for this problem?
10. A heavy packing crate accidently falls from an airplane at the instant the airplane is directly above a house. Is the house in danger of being hit? Explain why or why not.
How does the crate fall from the point of view of someone in the plane? In other words, what does the falling crate look like from the plane's frame of reference? Assume no air resistance.
What does the crate's path of fall look like from the point of view of someone standing on the ground? Draw a picture to illustrate.
If a plane is 1000 meters in the air traveling at 150 m/s and wants to drop a bucket of water on a burning building, how far from the building should it be dropped if we assume no air resistance? (x = 2143 m).
What if the plane had to drop the bucket 1800 meters from the tree above? How fast must the plane be traveling? (126 m/s)
11. For a projectile shot at an angle up into the air, what two things is it doing simultaneously?
For the first half of the flight, what is happening to the vertical velocity and why?
For the second half of the flight, what is happening to the vertical velocity and why?
A projectile is shot with a velocity of 200 m/s 30 degrees Above the Horizontal. Answer the following questions.  a. Find the maximum height of the object. (510 m)
b. Find the total time of flight of the object. (20.4 s)
c. Find the total horizontal distance of the object by using Vx = x/t and the other x equation given in class. (Conceptual physics: disregard the other equation). (3534 m)
d. For Honors Physics: Find the velocity of the ball at t = 6.0 seconds. (179 m/s 13° AH)
d. For Basic Physics: What is the vertical velocity of the cannon at 8.2 seconds. (Vy = 19.6 m/s)
e. For Honors Physics: When will the object have the same speed as found in part d, but opposite direction? (14.4 s)
e. For Basic Physics: When will the object have the same speed as found in part d, but opposite direction? (12.2 s)
f. Find the object’s final velocity, and explain why it is what it is. (200 m/s 30° BH)
12. No matter how you throw an object, how far does it fall from the path it would have taken if there was no gravity after one second?
How far after the third second?
Explain why 45 degrees yields the largest distance traveled based on the illustration on your lecture sheet.
Explain the last question but use the equation to defend your answer. (the x = V^2sin(2*angle)/9.8)
For Honors Physics only:
A ball is thrown at 20 m/s at an angle of 65 degrees above the horizontal. The ball leaves the thrower's hand at a height of 1.8 m. At what height will the ball strike a wall 10 meters away? (16.4 m) (Remember to use steps one and two of the problem solving steps if you are unsure about this problem).
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