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time zero, an object of mass m that is initially at rest is dropped from a tower of height h. The dimensions of the object are negligible compared to the size of the cart. A wheeled cart is moving in the –x direction at a constant speed vc. The entire apparatus is located on Earth's moon. The local gravitational acceleration constant is ag = 1.625 m/s². At the instant the object is released from the tower, the distance from the front-end of the cart to the object's anticipated impact point on the lunar surface is L. You are interested in the range of L values that ensures the object will fall directly into the cart. m = 5.00 mg, Initially at rest h = 55 m Impact point Lc = 3 m vc = 9.5 m/s hc = 1.5 m L= ?- You may assume the entire length of the cart is available for capturing the object, i.e., it has very thin walls. All numeric values in the diagram are measured, so significant figures are important when calculating results. You are allowed to assume the initial speed of the resting object is exactly zero. a) The Newtonian equation of motion for the falling object in the vertical direction is: 1 ? +v,of + Yo, where t is the time, v,o is the initial speed in the y-axis direction, and yo is the initial height. Starting at time zero, at what later time t will the object fall to the same height as the cart? b) What is the maximum initial distance that L can be to catch the object in the cart? Hint: Consider the uncertainty in the calculated L due to the uncertainty in the cart speed and the uncertainty in the derived time from Part (a).

time zero, an object of mass m that is initially at rest is dropped from a tower of height h. The dimensions of the object are negligible compared to the size of the cart. A wheeled cart is moving in the –x direction at a constant speed vc. The entire apparatus is located on Earth's moon. The local gravitational acceleration constant is ag = 1.625 m/s². At the instant the object is released from the tower, the distance from the front-end of the cart to the object's anticipated impact point on the lunar surface is L. You are interested in the range of L values that ensures the object will fall directly into the cart. m = 5.00 mg, Initially at rest h = 55 m Impact point Lc = 3 m vc = 9.5 m/s hc = 1.5 m L= ?- You may assume the entire length of the cart is available for capturing the object, i.e., it has very thin walls. All numeric values in the diagram are measured, so significant figures are important when calculating results. You are allowed to assume the initial speed of the resting object is exactly zero. a) The Newtonian equation of motion for the falling object in the vertical direction is: 1 ? +v,of + Yo, where t is the time, v,o is the initial speed in the y-axis direction, and yo is the initial height. Starting at time zero, at what later time t will the object fall to the same height as the cart? b) What is the maximum initial distance that L can be to catch the object in the cart? Hint: Consider the uncertainty in the calculated L due to the uncertainty in the cart speed and the uncertainty in the derived time from Part (a).

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Please help with questions a and b.

At time zero, an object of mass m that is initially at rest is dropped from a tower of height h. The dimensions of the object are negligible compared to the size of the cart. A wheeled cart is moving in the -x direction at a constant speed vc. The entire apparatus is located on Earth's moon. The local gravitational acceleration constant is ag = 1.625 m/s². At the instant the object is released from the tower, the distance from the front-end of the cart to the object's anticipated impact point on the lunar surface is L. You are interested in the range of L values that ensures the object will fall directly into the cart. m = 5.00 mg, Initially at rest h = 55 m Impact point Lc = 3 m vc = 9.5 m/s hc = 1.5 m L= ? You may assume the entire length of the cart is available for capturing the object, i.e., it has very thin walls. All numeric values in the diagram are measured, so significant figures are important when calculating results. You are allowed to assume the initial speed of the resting object is exactly zero. a) The Newtonian equation of motion for the falling object in the vertical direction is: 1 y(t) = -at +v,oft + yo, where t is the time, v,o is the initial speed in the y-axis direction, and yo is the initial height. Starting at time zero, at what later time t will the object fall to the same height as the cart? b) What is the maximum initial distance that L can be to catch the object in the cart? Hint: Consider the uncertainty in the calculated L due to the uncertainty in the cart speed and the uncertainty in the derived time from Part (a).
Transcribed Image Text:At time zero, an object of mass m that is initially at rest is dropped from a tower of height h. The dimensions of the object are negligible compared to the size of the cart. A wheeled cart is moving in the -x direction at a constant speed vc. The entire apparatus is located on Earth's moon. The local gravitational acceleration constant is ag = 1.625 m/s². At the instant the object is released from the tower, the distance from the front-end of the cart to the object's anticipated impact point on the lunar surface is L. You are interested in the range of L values that ensures the object will fall directly into the cart. m = 5.00 mg, Initially at rest h = 55 m Impact point Lc = 3 m vc = 9.5 m/s hc = 1.5 m L= ? You may assume the entire length of the cart is available for capturing the object, i.e., it has very thin walls. All numeric values in the diagram are measured, so significant figures are important when calculating results. You are allowed to assume the initial speed of the resting object is exactly zero. a) The Newtonian equation of motion for the falling object in the vertical direction is: 1 y(t) = -at +v,oft + yo, where t is the time, v,o is the initial speed in the y-axis direction, and yo is the initial height. Starting at time zero, at what later time t will the object fall to the same height as the cart? b) What is the maximum initial distance that L can be to catch the object in the cart? Hint: Consider the uncertainty in the calculated L due to the uncertainty in the cart speed and the uncertainty in the derived time from Part (a).
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