Use the following guide to help prepare for your upcoming exam:
On the exam, you will be given the Quadratic Equation and the Equation for displacement for uniform acceleration; these were the equations given on the last exam.
Problems with Answers:
1. A cross-country skier skis 1.00 km north and then 2.00 km east. Assuming you’re your coordinate system defines the x-axis to the east and y-axis to the north, what is the magnitude and direction of her displacement in both component vector and polar notation? [ans: (2.00 km)î + (1.00 km)ĵ and 2.24 km at 26.6º above the x-axis]
2. A baseball hits the ground at a speed of 48 m/s at an angle of 30º above the ground. What are the horizontal and vertical components of the ball’s velocity? [ans: vertical– 24 m/s; horizontal – 42 m/s]
3. At the state science fair, you are given the opportunity to dig up the keys to a new car. You have only once chance to dig a hole. The instructions state that from the starting point, the keys are buried at a spot at the sum of the following displacements:
72.4 m at 32.0º east of north;
57.3 m at 36.0º south of west;
17.8 m due south.
Use component vector addition to identify the correct location.
[ans: (-7.99 m)î + (9.92 km)ĵ or 12.7 m at 39º west of north]
4. A motorcycle stunt rider rides off the edge of a cliff. Just at the edge, his velocity is horizontal, with a magnitude of 9.0 m/s. Find the motorcycle’s position (assume cliff edge to be the origin and velocity after 0.5 s. [ans: Dx = 4.5 m, Dy = -1.2 m (or 4.7 m @ 14.9º below horizontal) and vx = 9.0 m/s, vy = -4.9 m/s (10.2 m/s @ 29º below horizontal)]
5. A military helicopter on a training mission is flying horizontally at a speed of 60.0m/s and accidentally drops a bomb (a dumb one, not on of the fancy guided ones). When the helicopter dropped the bomb, it was at an elevation of 300 m above the earth’s surface. How long does it take the bomb to reach the ground? [ans: 7.82 s] How far does it travel horizontally before it hits the ground? [ans: 469 m] What is the magnitude of the displacement of the bomb when it hits the ground? [ans: 557 m]
6. A foolish physics major dives off a cliff with a running horizontal leap, as shown in the figure to the right. What must his minimum speed be as he leaves the cliff so that he clears the ledge at the edge of the lake? [ans: 1.29 m/s]
7. A shot putter releases the shot (heavy metal ball) some distance above the level ground with a velocity of 12.0 m/s at an angle of 51.0º above the horizontal. The shot hits the ground 2.08 s later. What are the components of the initial velocity? [ans: vert – 9.33 m/s, horiz – 7.55 m/s] How high was the shot when it was released? [ans: 1.79 m] What is the total velocity at impact with the ground? [ans: vert – -11.05 m/s, horiz – 7.55 m/s OR 13.4 m/s @ 55.6º above the horizontal]
Any introductory physics book in the library will have lots of other examples of 2D motion, if you want to seem some more.
Good Luck!!!!
Dr. D
8. The graph below shows the population of the city of Pittsburg, PA since 1800. It uses the results of the census, and includes an estimate from 2005. Answer the questions below:
- What was the greatest population for the city? (ans: ~680,000)
- When was the greatest rate of population change? (ans: 1900 – 1910)
- What was the greatest rate of population change? (ans: ~22,000 people/year)
- By what percentage has the population changed from the maximum to the most recent data? (ans: 53%)
9. Plot the following sets of points on an x-y coordinate system and identify their shapes:
- (0,0), (2,6), (3,9), (5,15) (ans: straight line)
- (4,-2), (-1,3), (-1,-2), (4,3) (ans: square)
- (5,-3), (-3,-3), (5,7), (0,-3), (5,2) (ans: right triangle)
- (2,1), (-3,1), (2,7), (-3,7) (ans: rectangle)
10. Gary runs from point (2,3) to (3,-4) in 5.2 s. In the same amount of time, Frank runs from (2,1) to (-2,-3). Who is the faster runner and how fast is he running? Note, distances are in meters. (ans: Gary @ 1.4 m/s)
11. Write the initial and final positions of Gary and Frank in polar coordinates. (ans: Gary: 3.6 m @ 56.3º above +x axis to 5.0 m @ 53.1º below +x axis (or -53.1º) Frank: 2.24 m @ 26.6º above x axis to 3.6 m @ 56.3 below –x axis (or -123.7º)
12. Spotting a CHP officer, you brake your Ford Pinto from 105 km/h to 82 km/h. It takes 3 s for this to occur. What is your acceleration? (ans: 27.6 m/s2 appx 2.8g’s!)
13. A baseball player tosses a ball straight up in the air with an initial speed of 12 m/s. How long does the ball take to reach its maximum height? (ans: 1.2 s)
14. How high does the ball go above the release point? (ans: 7.3 m)
15. How long does it take for the ball to reach a point 5.0 m above its release point? (ans: 0.53 s AND 1.9 s – it passes by this height twice, once up and once down).
16. At the instant that a traffic light turns green, an automobile starts with a constant acceleration of 2.2 m/s2. At the exact same moment, a truck traveling with a constant speed of 9.5 m/s passes the automobile. How much time will elapse before the car catches back up to the truck? (ans: 8.6 s)
17. How far is the car from the traffic light when it catches the truck? (ans: 82 m)
18. The car and truck continue to drive under the conditions in Problem 15. After another interval of time equal to the “catch up time,” how far ahead of the truck is the car? (ans: 162 m)