Name: Class: Physics Teacher: Mr. Szopiak Date: Midterm Exam: Making a Study Guide This worksheet will help you and your classmates put together a pretty comprehensive guide to your midterm studying. Your task is to first select 3 questions from each section. You should fully work out each problem on a separate sheet of paper cleanly and neatly. You should also provide helpful comments on each step that you take. By pooling all of these together among the class, you will be able to form a really solid study guide for yourselves (Plus, this will be your opportunity to earn points back on your last test) SECTION I: KINEMATIC QUANTITIES 1. You decide to run from your house to a friend s house that is 3 miles away. You then walk home. (a) What distance do you travel? (b) What was your displacement for the entire trip? (c) Using this example, explain how distance and displacement are two different quantities used to describe the changing of location. 2. True or False: An object can be moving for 10 seconds and still have zero displacement? (a) If the above statement is true, then describe example of such a motion. If the above statement is false, then explain why it is false. (b) How do we often represent the quantity displacement in the x-direction? Be sure to explain what all the symbols you use mean. 3. True or False: It is possible for an object to move for 10 seconds at a high speed and end up with an average velocity of zero. (a) If the above statement is true, then describe example of such a motion. If the above statement is false, then explain why it is false. (b) How is speed different than velocity? (c) How are the equations for calculating speed and velocity different? What can we learn about speed and velocity from these equations? 4. You run from your house to a friend s house that is 3 miles away in 30 minutes. You then immediately walk home, taking 1 hour on your return trip. (a) What is the average speed (in mi/hr) for the entire trip? (b) What was the average velocity (in mi/hr) for the entire trip? (c) What is the instantaneous velocity at t = 22 min? (d) Which of the above quantities must include a direction? 5. While playing fetch with your dog, you decide to calculate the speed and velocity at which it can run. (a) On the first throw, you throw it 60 m away, and the dog zig-zags to where the ball is thrown and then stops. Which value is higher the average speed or the average velocity of your dog? Explain what practical information these two values give you. (b) On the second throw to the same spot 60 m away, the dog runs straight to the ball. Calculate the average speed and average velocity. Compare the magnitudes of average speed and the average velocity. What do you notice about these quantities in this situation? 6. Wile E. Coyote is chasing after the roadrunner. The roadrunner travels at an average speed of 53 mph, while Wile E. Coyote travels at an average speed of 46 mph.
Worksheet: Midterm Study Guide Page 2 of 6 (a) Convert both average speeds into m/s using dimensional analysis. (b) How long, in seconds, does it take the roadrunner to run a straight distance of 750 m? (c) How long, in seconds, does it take the Wile E. Coyote to run that same distance? (d) The edge of a cliff is 750 m away. Wile E. Coyote runs in a straight line to the cliff, and (surprisingly) beats the roadrunner there by 10 seconds. What, then, is the overall distance travelled by the roadrunner? (e) What might the roadrunner s path from part (d) look like? 7. Your pet frog jumps 15 times a minute. Each jump covers a distance of 5 inches. (a) What is the average velocity of your frog, in in/min? (b) What is the average velocity of your frog in m/s? (c) If your frog jumps for 10 minutes in a straight line, what will its displacement be? 8. A car is moving backwards down a hill at -3.0 m/s when the driver gets the engine started. After 2.5 s, the car is moving uphill at a velocity of 4.5 m/s. (a) Calculate the car s average acceleration. (b) In a car, there are 3 controls that can cause a car to accelerate. What are they? Explain how each one causes the car to accelerate. (c) The units for acceleration are ordinarily m = position. This means that this object with this acceleration s 2 time 2. (Select all that apply. Explain why each one applies or does not apply.) i. Moves 3 meters in 1 second ii. Changes its velocity by 3 m/s in 1 s iii. Moves 30 meters in 10 seconds iv. Has a velocity of 27 m/s after 10 seconds 9. Using dimensional analysis, convert the following quantities to the target units. (a) 22.0 m s ft ms (b) 0.005 yd min 2 km day 2 (c) 350yrs s (d) 1.0 in s mi hr (e) 9.8 m s 2 mi yr 2 SECTION II: ONE-DIMENSIONAL HORIZONTAL KINEMATICS 10. An airplane accelerates down a runway at 3.20 m/s 2 for 32.8 s until it finally lifts off the ground. Determine the distance traveled before take-off. 11. A racecar accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. (a) Determine the acceleration of the car. (b) Determine the distance traveled. 12. Rennata Gas is driving through town at 25.0 m/s and begins to accelerate at a constant rate of -1.0 m/s 2. Eventually Rennata comes to a complete stop. How long does it take Rennata to roll to a stop? 13. A bullet leaves a rifle with a muzzle velocity of 521 m/s. While accelerating through the barrel of the rifle, the bullet moves a distance of 0.840 m. Determine the acceleration of the bullet (assume that it is uniform that is, the acceleration is the same throughout). 14. A runner is moving with a velocity of 4 m/s when she accelerates at 2 m/s 2 for 3 seconds. How fast is she traveling now? 15. In a football game, running back is at the 10-yard line and running up the field, (10, 20, 30, 40 yard line etc.) and runs for 3 seconds at 8 yd/s. What is his current position? 16. A bicyclist is traveling at 25 m/s when he begins to decelerate at 4 m/s 2. How fast is he traveling after 5 seconds?
Worksheet: Midterm Study Guide Page 3 of 6 17. An alien spaceship is 500 m above the ground and moving at a constant velocity up of 150 m/s. How high above the ground is the ship after 5 seconds? 18. A baseball is rolled horizontally along the ground at 45 m/s. The ball slows down at a rate of 5 m/s 2. How long is the ball rolling before coming to rest? SECTION III: POSITION-TIME & VELOCITY-TIME GRAPHS 19. Examine the above position-time graph and answer the following questions. (a) What is the position at t = 0, 1, 2, 3, 4, 5, and 6 seconds? (b) With a position-time graph, how do we calculate the velocity of the object? (c) What is the velocity for interval (A) of the graph? What about for intervals (B), (C), and (E)? (d) During which intervals is the object moving forward? During which intervals is the object stationary? (e) Which segment shows an acceleration? 20. Examine the above velocity-time graph and answer the following questions. (a) What is the velocity at t = 0, 1, 2, 3, and 4 seconds? (Check units) (b) With a velocity-time graph, how do we calculate acceleration? (c) What is the acceleration between t = 0 and 1 s? Between t = 2 and 3 s? What is the acceleration between t = 1 and 2 s? (d) When is the object stationary? (e) With a velocity-time graph, how do we calculate displacement? (f) What is the displacement of the object between t = 1 and 2 s?
Worksheet: Midterm Study Guide Page 4 of 6 21. Draw a velocity-time graph for problem #11. Be sure to identify all the relevant points. Use what you know about velocity-time graphs to find the acceleration of the racecar and its displacement. 22. Draw a position-time graph for problem #15. Be sure to identify all the relevant points. 23. Draw a position-time graph for problem #17. Be sure to identify all the relevant points. 24. Draw a velocity-time graph for problem #18. Be sure to identify all the relevant points. SECTION IV: ONE-DIMENSIONAL FREE-FALL KINEMATICS 25. Melissa threw a penny straight down off the Empire State building. The building is 354 m tall. If Melissa threw the penny down such that it left her hand at 35 m/s, (a) How fast will the coin be traveling when it hits the pavement? (b) How long does it take to hit the ground? 26. An hour later, after the sidewalk damage was cleaned up, Paul dropped a coin off the top of the Empire State building. (a) How fast will the coin be traveling when it hits the pavement? (b) How long does it take to hit the ground? 27. To calculate the depth of a well, a physics student drops a rock into the well. 4.5 seconds after the rock is dropped the student sees it hit the bottom. (a) How deep is the well? (b) How fast is the rock travelling the instant before it hits the bottom? 28. A rock is dropped on a newly explored planet. The rock is dropped 1.22 meters. The acceleration due to gravity is 1.3 m/s2. How much time did is take for the rock to fall? 29. A meteor falls from the sky to the Earth. The meteor already had an initial velocity downward when it was spotted. If it hit the Earth at 335 m/s after being seen for 30 seconds, then what was the initial velocity of the meteor? 30. An angry mob lynches a physics teacher after receiving their grades. They throw the physics teacher off a tall building. They throw the physics teacher straight down with a velocity of 20 m/s. The teacher falls for 3.0 seconds before landing on a stack of empty cardboard boxes. How high was he thrown from? 31. You throw a water balloon directly up into the air with an initial velocity of 21 m/s. (a) What is the velocity of the water balloon at its maximum height? (b) What is the maximum height of the water balloon? (c) How long does it take to reach the maximum height? (d) How long does it take to return to its original height (i.e. your head)? (e) What is the velocity of the water balloon when it reaches your head? SECTION V: VECTOR ADDITION 32. Jolly walks 5 meters eastward, then 10 meters westward, and then another 12 meters eastward. (a) Draw each of the three vectors separately and to scale (1.0 cm = 1.0 m). (b) Add the vectors together graphically. (c) Add the vectors together algebraically. (d) What is Jolly s overall displacement? (magnitude and direction) (e) Does the order of these vectors affect Jolly s overall displacement? Why or why not? (f) What is the distance that Jolly travels? 33. Jess goes for a run, 8 meters westward and then 13 meters southward. (a) Draw each of the three vectors separately and to scale (1.0 cm = 1.0 m). (b) Add the vectors together graphically.
Worksheet: Midterm Study Guide Page 5 of 6 (c) Add the vectors together algebraically. (d) What is Jolly s overall displacement? (magnitude and direction) (e) Does the order of these vectors affect Jolly s overall displacement? Why or why not? (f) What is the distance that Jolly travels? 34. Stewart is flying his plane due north (90 o ) at a velocity of 120 mph. His plane experiences a 40 mph wind that is directed at 150 o. Solve for the resultant velocity both graphically and algebraically. (magnitude and direction) 35. A remote control car travels 5 ft south, 5 ft east, 6.5 ft west, 5 ft north, 14 ft north, and then 3 ft east. Solve for the resultant displacement both graphically and algebraically. (magnitude and direction) SECTION VI: VECTOR COMPONENTS 36. Draw out each vector and decompose each into x- and y- components. Show all of your trigonometric work. (a) v i = 60 m s at 35o (b) v i = 22 m s at 140o (c) Δ x = 1402 m at 250 o (d) a = 10 m at 340 o s 2 37. Draw out each vector and decompose each into x- and y- components. Show all of your trigonometric work. (a) v i = 9.2 m s at 67o (b) v i = 451 m s at 12o (c) Δ x = 21.4 m at 330 o (d) a = 114 m at 90 o s 2 38. Draw out each vector and decompose each into x- and y- components. Show all of your trigonometric work. (a) v i = 3.0 m s at 0o (b) v i = 98 m s at 132o (c) Δ x = 63 m at 210 o (d) a = 0.045 m at 45 o s 2 39. A hiker hikes 5 km due east, then 6 km at a 30 o angle from the horizontal, and then hikes a final 13 km due south. (a) Draw all three vectors tip-to-tail (in whatever order). (b) Sketch the resultant vector (make it look bolded). (c) Solve for the resultant displacement algebraically. SECTION VII: INDEPENDENCE OF VECTORS [In this section, you must complete both questions.] 40. Mr. Szopiak is thinking of trying to swim across the Mississippi River rather than waiting in traffic for 15 minutes. The Mississippi River is 701 m wide, and Mr. Szopiak can swim at a speed of 1.5 m/s. The current is flowing at 4.0 m/s downstream. (a) Draw the vector for Mr. Szopiak s swimming velocity and the vector for the velocity of the river s current. (b) How long does it take Mr. Szopiak to get across the river? (c) How far downstream does the current carry Mr. Szopiak? (d) If Mr. Szopiak attempts to swim across, what will be his resultant velocity in the water? (e) What will his resultant displacement be?
Worksheet: Midterm Study Guide Page 6 of 6 41. Assume the same situation as the problem above. (a) If Mr. Szopiak can run at an average speed of 3 m/s, how long will it take him to run back to the point directly across from his starting point once he swims across? (b) Does Mr. Szopiak save time by swimming across the river? SECTION VIII: PROJECTILES 42. A ping-pong ball is launched horizontally off of a table 0.76 m high regulation-size ping-pong table. The ball lands on the ground 8 m away from the table. (a) How long was the ball in the air? (b) What was the ping-pong ball s initial velocity? (c) *Formulate and draw the following two functions: the function of x-position with respect to time, and the function of y-position with respect to time. (d) *Formulate and draw the following two functions: the function of x-velocity with respect to time, and the function of y-velocity with respect to time. 43. A baseball player hits a solid line drive (horizontally) from home plate with an initial velocity of 110 mph. Assume the ball is hit from 4 ft high. (a) How far is the ball away from home plate when it hits the ground for the first time? (b) If the outfield begins 155.5 ft from home plate, does the ball reach the outfield before the first bounce? (c) At what speed would the player have to hit the ball in order for him to hit the ball on a line (horizontally) out of the infield? 44. A penny is kicked horizontally off the roof of a ten-story building (33.3 m high). It is kicked at 22 m/s. (a) What is the penny s initial horizontal velocity? (b) What is the penny s initial vertical velocity? (c) How long is the penny in the air? (d) How far away from the building does the penny land? (e) What is the penny s resultant velocity when it hits the ground? 45. Mike Easter threw a javelin at 57 m/s and at an angle of 25 degrees with the ground. Neglect the height of the javelin when it was thrown. So it lands at the same height it is thrown from. (a) How long was it in the air? (b) How far along the ground did the javelin travel? (c) How fast, (direction and magnitude), was it traveling when it hit the ground? 46. The motorcycle daredevil Evil Kinevil is about to make a world record distance jump. He leaves the jump ramp at 45 m/s. The ramp is at a 22 angle with the ground. He lands at the same height he took off from. (a) How much time did he spend in the air? (b) What is the distance of his jump? (c) What is the maximum height of the jump? (d) What is his velocity when he lands? 47. Robbie Knievel is about to make another world record distance jump. He leaves the jump ramp at 45 m/s. The ramp is at a 68 (90-22 ) angle with the ground. He lands at the same height he took off from. (a) How much time did he spend in the air? (b) What is the distance of his jump? (c) What is the maximum height of the jump? (d) What is his velocity when he lands?