Honors Assignment - Kinematics
Reading Chapter 2
Objectives/HW
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The student will be able to: |
HW: |
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1 |
Define and distinguish the concepts scalar and vector. Make the connection between the visual representation of a vector and its numerical representation of magnitude and direction angle. |
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2 |
Define, distinguish, and apply the concepts: distance, displacement, position. |
1, 2 |
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3 |
Define, distinguish, and apply the concepts: average speed, instantaneous speed, constant speed, average velocity, instantaneous velocity, constant velocity. |
3 – 7 |
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4 |
Define, distinguish, and apply the concepts: average acceleration and instantaneous acceleration, and constant acceleration. |
8 – 16 |
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5 |
State the displacement and velocity relations for cases of constant acceleration and use these to solve problems given appropriate initial conditions and values. |
17 – 28 |
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6 |
State and use the conditions of freefall, including the value of g, to solve associated problems. |
29 – 41 |
Homework Problems
1. A NASA team oversees a space shuttle launch at Cape Canaveral and then travels to Edward's Air Force Base in California to supervise the landing. Which group of people, the astronauts or the NASA team has the greater displacement? the greater distance?
2. Assume the field in
Neyland Stadium runs perfectly north and south. Beginning with an initial
position of 60.0 yds. , 90.0°
from the south goal post, Mr. M marches (in linear segments) the following four
displacements in succession: d1 = 10.0 yds, 0.0°,
d2 = 11.2 yds, 206.6°,
d3 = 11.2 yds, 333.4°,
d4 = 10.0 yds, 180.0°.
(a) Using a protractor and ruler measure out a diagram of Mr. M's
march. (b) From initial to final position what is the overall displacement?
(Hint: measure your diagram!) (c) From initial to final position what is the
total distance? (d) What is the final position?
3. The speed of light in
the vacuum of space or in air is a constant value of 3.00 x 108
m/s.
(a) A light-year is the distance traveled by light in one year. What is this
distance?
(b) What amount of time does it take for light to travel from the Moon to the
Earth – a distance of 384 Mm? (c) How much time would it take a car traveling
45 m/s (100 mph)?
4. An airport radar uses
the reflection (or "echo") of a radio signal to measure aircrafts'
positions. Suppose the position of a certain helicopter at 1:00 PM is 105 miles, 90.0° from the airport. At 1:30 PM it is 48 miles, 90.0° from the airport. (a)
Find the displacement of the helicopter over this interval of time. (b) Find
the average velocity of the helicopter.
(c) Assuming the velocity remains constant what is the position of the
helicopter at 1:45 PM? Note: a diagram showing the airport and helicopter is very
helpful!
5. You are driving down a street in a car at 55 km/h. Suddenly a child runs into the street. If it takes you 0.75 s to react and apply the brakes, how many meters will you travel before you begin to slow down?
6. Suppose you need average speed of 100 km/h to arrive at a certain destination on time. However traffic limits your average speed to only 60 km/h during the first half of the trip’s distance. What must your average speed be in the second half of the trip to be on time?
7. The graph below shows
the motion of a hummingbird. For the interval of time shown, determine the
following: (a) What is the bird’s greatest distance away from the flower?
(b) What is the bird’s most western position? (c) At what point(s) in time is
the bird at the flower? (d) Determine the bird’s average velocity. (e)
Determine the bird’s average speed. (f) What is the bird’s velocity at 10.0
s? (g) What is the bird’s velocity at 5.5 s? (h) At what position(s) is the
bird’s velocity equal to zero? (i) What is the bird’s maximum speed?
8. Again refer to the above graph. (a) The bird is moving with a constant velocity at what point(s) in time? (b) The bird is accelerating at what point(s) in time? (c) The bird’s speed is decreasing at what point(s) in time?
9. Answer the following and explain or give an example: (a) Can an object have a speed equal to zero and at the same time an acceleration not equal to zero? (b) Can an object have a constant speed and a changing velocity? (c) Can an object have a constant velocity and a changing speed? (d) Can an object be moving but not accelerating? (e) Can an object have velocity and acceleration vectors that point in opposite directions?
10. A 1956 VW Van could go from 0 to 60 mph (26.8 m/s) in 75 seconds (as measured by Road & Track). (a) Determine the average rate of acceleration. (b) Assuming a braking deceleration of 9.0 m/s2 what amount of time was required to return from 60 mph to 0?
11. A 2010 Chevy Camaro went from zero to 20 mph, 40 mph, and 60 mph, in times of 1.1 s, 2.6 s, and 4.6 s respectively. This is an interesting pattern because the average acceleration changes by about the same percentage for every 20 mph faster the car goes. (a) By about what percent does the acceleration rate change per every 20 mph increase? (b) If the pattern continues, what time is required to go from 0 to 80 mph?
12. In the 1940’s rocket-powered sleds were used to test the responses of humans to acceleration. Suppose the sled reaches a speed of 222 m/s in 2.10 s and then in another 0.90 s is brought to a stop. Determine the greatest number of g's experienced by the rider. (A "g" is an acceleration rate equal to 9.80 m/s2.)
13. An F-22 fighter jet is flying at a “supercruise” speed of 545 m/s when the pilot kicks in the afterburners. The afterburners cause an acceleration rate of 3.47 m/s2. How much time is needed to reach a speed of 600 m/s (Mach 2.0 or twice the speed of sound!)?
14. A baseball with an initial velocity of 40.0 m/s, south undergoes an average acceleration of 1.15 ´ 105 m/s2, northward due to the impact of a bat that is in contact with the ball for 0.75 milliseconds. What is the final velocity of the ball?
15. The graph below shows
the motion of an object. For the interval of time shown, determine the
following: (a) At what point(s) in time is the object moving southward? (b)
Find the maximum speed. (c) Find the average acceleration from t = 16 s
to t = 32 s. (d) Find the acceleration at t = 4.0 s and state
whether speed is increasing or decreasing at that point.
(e) Find the acceleration at t = 26 s. (f) The acceleration is zero at
what point(s) in time?
(g) The speed of the object is decreasing at what point(s) in time?
16. Using the same graph (shown above), determine the displacement of the object during the following intervals of time: (a) from 0 to 12 s, and (b) from 20 to 32 s. (c) Determine the distance traveled by the object from 0 to 50 s.
17. A skateboarder starts from rest atop a slope that is 20.0 m long and accelerates uniformly 2.60 m/s per second down the slope. (a) What is the position of the skateboarder 3.00 s later? (b) What is the speed at that point? (c) How much time overall is needed to go down the slope?
18. The maximum deceleration rate of a typical car is about 10 m/s2.(a) Determine the distance required to stop your car when initially traveling 30.0 m/s. (b) Repeat for a speed 41.4% faster – 42.3 m/s.
19. You are investigating an accident scene in which several cars wrecked in order to avoid a car skidding to a stop. The skid marks are 65 m long. A skidding car will have a deceleration rate of about 10 m/s2. How fast was this car going before it began to skid?
20. An object traveling on a horizontal surface with an initial velocity of 12.0 m/s to the right is then accelerated 3.00 m/s2 towards the left. (a) Calculate the magnitude of this object's displacement at values of time: 0.00, 4.00, and 8.00 s. (b) Calculate the speed for the same times. (c) Describe the motion of the object for this time interval.
21. At t = 0.00 s a ball is
started rolling up an inclined plane with an initial velocity of 6.00 m/s, 15.0°. At t = 2.00 s the ball reverses its
direction and begins to roll back down. (a) How far up the slope does the ball
travel? (b) Find the ball's acceleration. (c) Find the speed of the ball at t
= 3.00 s. (d) Find the distance traveled by the ball during these 3.00
seconds.
(e) Find the ball's position at t = 3.00 s.
22. (a) Determine the displacement of a plane traveling northward that is uniformly accelerated from 66 m/s to 88 m/s in 12 s. (b) Repeat the calculation for the same plane slowing down from 88 m/s to 66 m/s in 12 s and show that the result is the same.
23. The bullet leaves the muzzle of a Glock 17 pistol with a speed of 375 m/s. The barrel of the pistol is 11.4 cm long. Find the acceleration rate of the bullet passing through the barrel.
24. A moving car decelerates for 5.0 s and comes to a complete stop. It travels 75 m in the process. (a) Determine its initial value of speed. (b) Determine its rate of deceleration.
25. The driver of a van “times the light” and passes through an intersection at constant speed 15.0 m/s just as the light turns green. At the same time a car in the adjacent lane accelerates from rest at 3.0 m/s2. (a) What distance must the car travel in order to catch up to the van (and then pass)? (b) What is the speed of the car as it passes the van?
26. Highway safety engineers design "soft" crash barriers so that cars hitting them will slow down at a safe rate. A person wearing a safety belt can withstand a deceleration rate of 300 m/s2. How thick should barriers be to safely stop a car that hits the barrier at 110 km/h and then slows to a stop as it crashes through and destroys the barrier?
27. A professional baseball pitcher throws a fastball at a speed of 44 m/s. The acceleration occurs as the pitcher holds the ball and moves it through a distance of about 3.5 m during the entire delivery motion. Calculate the acceleration rate, assuming it is uniform.
28. A driver of a car going 25.0 m/s suddenly notices a stop sign 40.0 m ahead. The braking deceleration rate of the car is 10.0 m/s2, but it takes the driver 0.75 s (reaction time) to get the brakes applied. (a) Determine if the car runs the stop sign. (b) Determine the maximum initial speed at which the car could be moving and manage to stop at the sign.
29. Under what circumstances
is the effect of air resistance negligible on a falling object?
i.e. When is the use of g = 9.80 m/s2 most valid?
30. One rock is dropped from a cliff, a second rock is thrown downward. When they reach the bottom, which rock has a greater speed? Which has a greater acceleration? Which reaches the ground in the least amount of time?
31. A stone is dropped into a very deep hole in the ground and it hits the bottom after falling for 2.80 s. (a) How deep is the hole? (b) What is the impact velocity of the stone?
32. Suppose a person drops
20.0 m (about 5 floors) from a burning building and onto an air bag. (a) What
will be the person's maximum speed during their fall?
(b) Repeat for a drop of 40.0 m.
33. A ball is thrown upward with an initial speed of 15.0 m/s. (a) Find the maximum height attained by the ball. (b) How much time does it take to reach the maximum height? How much time does it take to fall back down? (c) What is the ball's velocity when it reaches its initial position?
34. A punter goofs and punts
the football straight up. The hang time (total time in the air) is
4.00 s. (a) What height does the ball reach? (b) What initial velocity in
miles per hour does the ball have?
35. A kangaroo jumps to a vertical height of 2.8 m. What is its total time in the air?
36. A juggler throws a beanbag straight up into the air with initial speed 6.00 m/s. The beanbag leaves the juggler's hand 1.50 m above the floor. The juggler fails to catch the beanbag as it falls to the floor. (a) How long is the beanbag in the air? (b) What is its impact speed?
37. Someone in a skyscraper drops an egg on the boss’s car. The boss is mad. He asks you to investigate. You discover that a running video camera in the building recorded the egg passing by a 20th floor full-length window that is 3.00 m from ceiling to floor. Reviewing the tape you notice it takes 0.20 s for the egg to pass the window. Each “story” or “floor” of the building is 4.00 m. (a) From how high above the top of the window was the egg dropped? (From which floor?) (b) With what speed did the egg hit the car’s roof? (which was level with the floor of the 1st floor)
38. As a part of a movie stunt a stunt man hangs from the bottom of an elevator that is rising at a steady rate of 1.10 m/s. The man lets go of the elevator and drops in freefall for 1.50 s before being caught by a rope that is attached to the bottom of the elevator. (a) Calculate the speed of the man at the instant he is caught by the rope. (b) How long is the rope? (c) How much closer to the ground is the man at the instant he is caught by the rope than he was at the instant he let go of the elevator?
39. A tennis ball is dropped from 1.20 m above the ground. It rebounds to a height of 1.00 m. (a) With what velocity does it hit the ground? (b) With what velocity does it leave the ground? (c) If the ball were in contact with the ground for 0.010 s find its acceleration while touching the ground. (i.e. the acceleration of the "bounce")
40. Choose and solve one
of the following problems from your book pp. 42 – 47:
Chapter 2, Problems 12, 21, 22, 26, 28, 30, 40, 47, 60, 62, 64, 68, or 70
41. Choose and solve another one of the problems listed above.