36. Suppose the position vector for a particle is given as a function of time by 7(t) = x(t)î+ y(t)j, with x(t)%3D at + b and y(t)= ct +d, where a= 1 m/s, b= 1 m, c = 0.125 m/s, and d= 1 m. a) Calculate the average velocity during the time interval from t-2 s to t= 4 s. b) Determine the velocity and the speed at t=2s.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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accele
LABORATORY ACTIVITIES
7. Place a penny at the corner of a table as shown in the overhead view. Place a ruler next to the
penny and another penny on the top of the part of the ruler that hangs off the edge of the table.
Hold the end of the ruler on the table with one hand and use your other hand to flick the end of
the ruler with the penny parallel to the table surface. This will project the penny sitting on the
corner of the table in a horizontal direction. At the same time, the ruler will slide out from under
the second penny, which will fall straight down. Using your smartphone audio recorder, make an
audio recording of the two falling pennies. From the recording, determine the time interval
between the landings of the two pennies on the floor.
8. Select a wide wall for this activity. Cover you wall area with sheets of newspaper to keep the
wall free from chalk marks. Face the wall with your nose nearly touching it. Holding a small
piece of chalk in your hand, reach up as high as you can without tiptoeing and make a small
mark on the newspaper. From a standing or running start, jump up as high as you can and stretch
up as far as you can with your arm. At the top of your jump, make another mark on the
newspaper with the piece of chalk. With the meterstick, measure the vertical distance between
the two marks in meters. Using the equations of free-fall motion (up and down) and the
maximum height reached from this activity, calculate
a) your initial upward or take-off velocity
b) the time required for you to reach the maximum height
20 | Page
Transcribed Image Text:accele LABORATORY ACTIVITIES 7. Place a penny at the corner of a table as shown in the overhead view. Place a ruler next to the penny and another penny on the top of the part of the ruler that hangs off the edge of the table. Hold the end of the ruler on the table with one hand and use your other hand to flick the end of the ruler with the penny parallel to the table surface. This will project the penny sitting on the corner of the table in a horizontal direction. At the same time, the ruler will slide out from under the second penny, which will fall straight down. Using your smartphone audio recorder, make an audio recording of the two falling pennies. From the recording, determine the time interval between the landings of the two pennies on the floor. 8. Select a wide wall for this activity. Cover you wall area with sheets of newspaper to keep the wall free from chalk marks. Face the wall with your nose nearly touching it. Holding a small piece of chalk in your hand, reach up as high as you can without tiptoeing and make a small mark on the newspaper. From a standing or running start, jump up as high as you can and stretch up as far as you can with your arm. At the top of your jump, make another mark on the newspaper with the piece of chalk. With the meterstick, measure the vertical distance between the two marks in meters. Using the equations of free-fall motion (up and down) and the maximum height reached from this activity, calculate a) your initial upward or take-off velocity b) the time required for you to reach the maximum height 20 | Page
the Earth as it moves in its orbit around the Sun?
nat is the angular speed of the Earth in its orbit around the Sun?
EXERCISES
A ball is thrown horizontally from a height of 5.50 m with an initial speed of 25 m/s.
a) How long will it take the ball to reach the ground?
b) At what horizontal distance from the point of release will it strike the ground?
c) What will be the magnitude of its velocity when it strikes the ground?
d) At what direction will i strike the ground?
36. Suppose the position vector for a particle is given as a function of time by 7(t) = x(t)î +
y(t)j, with x(t)3D at + b and y(t)= ct +d, where a= 1 m/s, b= 1 m, c = 0.125 m/s, and d=D 1 m.
a) Calculate the average velocity during the time interval from t-2 s to t= 4 s.
b) Determine the velocity and the speed att=2s.
37. The vector position of a particle varies in time according to the expression? = 3î - 6î, where
ř is in meters and t is in seconds.
a) Find an expression for the velocity of the particle as a function of time.
b) Determine the acceleration of the particle as a function of time.
c) Calculate the particle's position and velocity at t-1s.
38. Mayan kings and many school sports teams are named for the puma, cougar, or mountain
lion- Felis concolor- the best jumper among animals. It can jump to a height of 12 ft when
leaving the ground at an angle of 45°. With what speed, in SI units, does it leave the ground to
make this leap?
39. The astronaut orbiting the Earth is preparing to dock with a Westar VI satellite. The satellite
is in circular orbit 600 km above the Earth's surface, where the free-fall acceleration is 8.21 m/s
Take the radius of the Earth as 6400 km. Determine the speed of the satellite and the time
interval required to complete one orbit around the Earth, which is the period of the satellite.
40. A tire 0.500 m in radius rotates at a constant rate of 200 rev/min. Find the speed and
acceleration of a small stone lodged in the tread of the tire (on its outer edge).
%3D
2.
%3D
LABORATORY ACTIVIȚTIES
Transcribed Image Text:the Earth as it moves in its orbit around the Sun? nat is the angular speed of the Earth in its orbit around the Sun? EXERCISES A ball is thrown horizontally from a height of 5.50 m with an initial speed of 25 m/s. a) How long will it take the ball to reach the ground? b) At what horizontal distance from the point of release will it strike the ground? c) What will be the magnitude of its velocity when it strikes the ground? d) At what direction will i strike the ground? 36. Suppose the position vector for a particle is given as a function of time by 7(t) = x(t)î + y(t)j, with x(t)3D at + b and y(t)= ct +d, where a= 1 m/s, b= 1 m, c = 0.125 m/s, and d=D 1 m. a) Calculate the average velocity during the time interval from t-2 s to t= 4 s. b) Determine the velocity and the speed att=2s. 37. The vector position of a particle varies in time according to the expression? = 3î - 6î, where ř is in meters and t is in seconds. a) Find an expression for the velocity of the particle as a function of time. b) Determine the acceleration of the particle as a function of time. c) Calculate the particle's position and velocity at t-1s. 38. Mayan kings and many school sports teams are named for the puma, cougar, or mountain lion- Felis concolor- the best jumper among animals. It can jump to a height of 12 ft when leaving the ground at an angle of 45°. With what speed, in SI units, does it leave the ground to make this leap? 39. The astronaut orbiting the Earth is preparing to dock with a Westar VI satellite. The satellite is in circular orbit 600 km above the Earth's surface, where the free-fall acceleration is 8.21 m/s Take the radius of the Earth as 6400 km. Determine the speed of the satellite and the time interval required to complete one orbit around the Earth, which is the period of the satellite. 40. A tire 0.500 m in radius rotates at a constant rate of 200 rev/min. Find the speed and acceleration of a small stone lodged in the tread of the tire (on its outer edge). %3D 2. %3D LABORATORY ACTIVIȚTIES
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