Concept explainers
The velocity vectors for blocks A and B are shown for a time immediately before release.
Draw a change in velocity vector for each block for a small time interval
Explain how Newton’s second law and the definition of acceleration can be used to determine the direction of the change in velocity vectors.
By what factors is the magnitude of
How does
Would this comparison change if we considered:
- another interval of time, equally small, occurring much later?
- a much larger time interval? Explain.
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- Page The heights of a rock after t seconds, when propelled straight up with an initial speed of 80 feet per second from an initial height of 20 feet, can be modeled by the function s(t) = -16t² + 80t +20. When will the height of the rock be 50 feet? Round your answer to the nearest tenth of a second. Carrow_forwardIn 2070, Adam wins a vacation at the new Moon Country Club. While vacationing Adam hits a golf ball off a cliff 300 meters high with an initial speed of 40 meters per second at an angle of 45° to the horizontal on the Moon(gravity on the Moon is one-sixth of that on Earth). Round all answers to three decimal places. a. Find parametric equations that describe the position of the ball as a function of time, t (round coefficients to three decimal places). b. How long is the ball in the air? c. When is the ball at its maximum height? What is that maximum height? d. When the ball lands, how far is it from Adam(the horizontal distance the ball traveled)?arrow_forwardThe position vector (in Cartesian Coordinates) of a particle is given by the function r(t) = ( (1/3) cos t^3 , (1/3) sin t^3 ) m where time is measured in seconds. Based on this information, answer the questions below. a) What is the radius of the circle that the particle moves along? b) What is the velocity of the particle as a function of time? c) What is the speed of the particle as a function of time? d) At time t = 2 sec, what is the acceleration of the particle in tangential and normal components?arrow_forward
- This is a two part problem. If you drive your car for 30 miles to the west, then 20 miles north of east at 60 degrees and then 5 miles south: A. What is the displacement of your car from the origin in unit vector notation? Draw a diagram to go along with your answer. B: What is the magnitude and direction of the displacement?arrow_forwardActivity 1.12- Vector Problems I 1. The final push to the summit of Mt. Everest starts at Camp 3. Your displacement from Camp 3 to Camp 4 is 400- meter west, 600-meter south, and 100 meter up. From Camp 4 to the peak is 900-meter east, 200-meter south, and 200 meter up. a. What is the displacement vector from Camp 3 to the peak of Mt. Everest? Give distances east/west, north/south and up/down from Camp 3 to the peak. b. What is the straight-line distance from Camp 3 to the peak of Mt. Everest? The straight-line distance is the distance if you drew a straight line from Camp 3 to Mt. Everest. 2. A spinning ball is falling straight downwards at 5 m/s bounces off the floor. Immediately after losing contact with the floor, the ball is moving at 4 m/s at 30° from vertical as shown. The ball is in contact with the floor for 0.15 a. Write the velocity vector of the ball just before the bounce in component vector form, ie, using unit vectors I and/or /. b. Write the velocity vector of the ball…arrow_forwardC. Draw or locate properly the following vector directions in the given Cartesian plane. Use protractor to measure the angle. A 40° north of east B 59' south of west C 15' south of east D 30° west of north D. A student runs initially at 3 m/s to the north, and suddenly accelerates at 4 m/s to the East. Find his resultant velocity (magnitude and direction). Show all your solution.arrow_forward
- A golf ball is struck with an initial velocity of 10m/s at an angle of 30 degrees above the horizontal. Please draw a picture of the situation in a 2-dimensional coordinate system. Please draw one ball at the initial position and one at the maximum height of the trajectory. We will call that maximum height the 'final position' for this example. Label Xi, yi Draw and label the vectors Vi, Viy, and Vix for the 'initial' state of the ball.arrow_forwardA golf ball is struck with an initial velocity of 10m/s at an angle of 30 degrees above the horizontal. Please draw a picture of the situation in a 2-dimensional coordinate system. Please draw one ball at the initial position and one at the maximum height of the trajectory. We will call that maximum height the 'final position' for this example. Label Xi, yi Draw and label the vectors Vi, Viv, and Vix for the 'initial' state of the ball. Label Xf, Yf Draw and label the vectors Vf, Vfy, and Vfx for the 'initial' state of the ball. Be sure to draw your vectors in the appropriate direction and with roughly the appropriate scale. Remember that, for projectile motion, the acceleration in the x direction is zero and the acceleration in the y direction is -g. Keep that in mind when you are deciding how to draw your velocity vectors.arrow_forwardWhich of the following statements is incorrect? O A scalar quantity specifies both the magnitude and unit. O In a coordinate system, the x-component in quadrant 1 is always positive. O A vector quantity specifies both the magnitude and direction. Distance and displacement are always equal in magnitude. O Acceleration is a rate of change of velocity.arrow_forward
- A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by = [5.00 m/s - (0.0180 m/s³)t²] i + [2.00 m/s + (0.550 m/s²)t]j. v = 7.00 Submit Previous Answers ✓ Correct Part D What is the direction (in degrees counterclockwise from +-axis) of the velocity of the car at t = 6.50 s? Express your answer in degrees. 0₂ = 52.7 ° Submit ✓ Part E a = Previous Answers Correct What is the magnitude of the acceleration of the car at t = 6.50 s? Express your answer with the appropriate units. 0.357 Submit μÀ m S ? Check the units used in your calculation; the numerical value you reached does not appear to have dimensions of acceleration. No credit lost. Try again. Previous Answers Request Answerarrow_forwardWe want to find the coefficient of restitution e between the ball and the floor. We will be able to measure the time of flight between subsequent bounces, but not the velocities before and after each impact. Question 1 a. Using the kinematics equation for position, find a relationship between the time of flight tn and the velocity of the ball after the nth bounce. You should obtain a quadratic equation that has two solutions for the time tm, but only one of them represents the time of flight. b. Using the kinematics equation for velocity and the relationship determined in the previous step, find the relationship between the velocity right after the nth bounce and the velocity right before the (n +1)th bounce? c. Given your answers to the previous parts of this question and the definition of €, find the coefficient of restitution e in terms of the subsequent times of flight tn and tr+1.arrow_forwardThe woman at C stands near the edge of a pier and pulls the rope horizontally at a constant speed of 6 ft/s. Find an equation for the speed of the boat as a function of the rope length AB as AB goes from 50 ft to 15 feet. Does the boat speed up, slow down, or move at a constant speed as it approaches the pier? A sketch or plot may be useful. 8 ft 6 ft/s Barrow_forward
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