A small lead ball, attached to a 1.45-m rope, is being whirled in a circle that lies in the vertical plane. The ball is whirled at a constant rate of three revolutions per second and is released on the upward part of the circular motion when it is 1.7 m above the ground. The ball travels straight upward. In the absence of air resistance, to what maximum height above the ground does the ball rise?[Input box labeled with an information icon and an exclamation mark followed by a dropdown menu with “m” as the selected unit of measure]

Given: The length of the rope is 1.45 m. The initial height of the ball is 1.7 m. The speed of the…

Answered: A small lead ball, attached to a 1.45-m…

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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A golfer hits a shot to a green that is elevated 3.30 m above the point where the ball is struck. The ball leaves the club at a speed of 18.4 m/s at an angle of 45.0˚ above the horizontal. It rises to its maximum height and then falls down to the green. Ignoring air resistance, find the speed of the ball just before it lands.
The drawing shows a version of the loop-the-loop trick for a small car. The radius of the loop r = 0.46 m. What is minimum initial speed (v) that the car needs to have in order to remain in contact with the circular track at all times? m/s
You are hiking in the rocky canyon lands of Utah and eventually realize you are lost. You climb up to stand on one of the tall rocks and shoot a flaming arrow into the air to signal your distress. You shoot the arrow with an initial speed of 30.0 m/s at an angle of 60.0° above the horizontal. The arrow hits the ground 7.50 seconds later. (Neglect air resistance.) (a) What maximum height does the arrow reach above its launch point? (b) Relative to the launch point, where does the projectile land? Give your answer in Cartesian (x,y) coordinates as well as polar (r,0) coordinates.
The figure shows two possible paths for negotiating an unbanked turn on a horizontal portion of a race course. Path A-A follows the centerline of the road and has a radius of curvature PA = 81 m, while path B-B uses the width of the road to good advantage in increasing the radius of curvature to PB = 189 m. If the drivers limit their speeds in their curves so that the lateral acceleration does not exceed 0.68g, determine the maximum speed for each path. 189 m Answers: (VA)max= (VB)max= i i 81 m m/s m/s
a skateboarder moving at 5.90 m/s along a horizontal section of a track that is slanted upward by θ = 46.0° above the horizontal at its end, which is 0.790 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height H to which she rises above the end of the track.
Two people swing jump ropes, as shown in the diagram. The highest point of the middle of each rope is M = 77 inches above the ground, and the lowest point is m 7 inches. The rope makes 4 revolutions per second. Write a model for the height h (in inches) of a rope as a function of the time t (in seconds) given that the rope is at its lowest point when t = 0. i ↑ h = h(t) = M Kit m -
A golfer hits a shot to a green that is elevated 2.60 m above the point where the ball is struck. The ball leaves the club at a speed of 17.3 m/s at an angle of 52.0° above the horizontal. It rises to its maximum height and then falls down to the green. Ignoring air resistance, find the speed of the ball just before it lands.
A grasshopper wants to jump over a thin vertical wall with the minimal possible jumping speed.The wall is h = 30 cm high and it is at distance d = 40 cm from the grasshopper. What should be the initial speed of the grasshopper? The gravitational acceleration is g = 9.8 m/s2 .Hint: The trajectory is not symmetrical to the wall. Express the starting speed v0 of the grasshopper in terms of the initial angle of elevation α, and then find the maximum of the v0(α) function
Some cats can be trained to jump from one location to another and perform other tricks. Kit the cat is going to jump through a hoop. He begins on a wicker cabinet at a height of 1.722 m above the floor and jumps through the center of a vertical hoop, reaching a peak height 3.130 m above the floor. (Assume the center of the hoop is at the peak height of the jump. Assume that +xaxis is in the direction of the hoop from the cabinet and +y axis is up. Assume g = 9.81 m/s2.) (a) With what initial velocity did Kit leave the cabinet if the hoop is at a horizontal distance of 1.550 m from the cabinet? (Express your answer in vector form. Give your answer to at least two decimal places for each vector component.) v0 =?m/s (b) If Kit lands on a bed at a horizontal distance of 3.580 m from the cabinet, how high above the ground is the bed?In m
A small child is learning to ride a bike for the first time. Her dad decides it would be a good idea to start her on a small hill. The hill is inclined at 3.40° to the horizontal. The child starts partway down the hill, 4.00 m away from her dad, who stays at the top. She starts to wobble, so her dad sprints toward her from rest with an acceleration of 3.80 m/s2. How far has the child gone before her parent catches her?
A ball is thrown eastward into the air from the origin (in the direction of the positive x-axis). The initial velocity is 40 i +64 k, with speed measured in feet per second. The spin of the ball results in a southward acceleration of 4 ft/s2, so the acceleration vector is a = -4 j - 32 k. Where does the ball land? (Round your answers to one decimal place.) X ft from the origin at an angle of 5.7 X from the eastern direction toward the south. 80.4 With what speed does the ball hit the ground? (Round your answer to one decimal place.) 61.3 X ft/s Submit Answer
The trajectory of a rock ejected from the Kilauea volcano, with a velocity of magnitude 63.9 m/s and at angle 12.1 degrees above the horizontal. The rock strikes the side of the volcano at an altitude of 90.6m lower than its starting point. Calculate the magnitude of the rock’s velocity at impact? Use g = 9.8 m/s2.

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