(a) Draw a diagram of the system when the jumper is below the equilibrium positionand moving up. Show all forces acting on the jumper and label them.(b) Find s, and hence relate h(t) to y(t).(c) Express the initial conditions in terms of y and y.(d) Solve for y(t).(e) Sketch h(t) versus t. 1. Jumping on a trampoline can be modelled by a mass-spring system. A person is jumpingon a trampoline vertically and lightly so that his/her feet do not leave the trampoline.offThe jumper has a mass of m = 50 kg. The natural height of the trampoline is 1.5 m aboveground level and the trampoline has a spring constant k = 1000 Nm¯¹. At equilibriumthe trampoline is compressed by a distance s metres.Natural heightSystem at equilibriumoff1.5mItTAir resistance acts on the jumper with a damping constant 3 = 50 N sm-¹. Assume thatthe gravitational constant is g = 10 ms ².Sm1.5mLet y(t) be the distance in metres of the jumper below the equilibrium position at timet seconds after the start of the jump, and let h(t) be the height in metres of the jumperabove ground level at time t. At time t = 0, the jumper starts at height 0.6 m above theground and the velocity of the jumper is 0.You may assume that the equation of motion for the system is50y + 50y + 1000y = 0.Please turn over

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Answered: 1. Jumping on a trampoline can be…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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人工知能を使用せず、すべてを段階的にデジタル形式で解決してください。ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT An object is thrown vertically upward from the ground with an initial velocity of 25 m/s. Determine a) The maximum height reached by the object. b) The time necessary for the object to return to the ground.
5. A ball is launched vertically into the air from a height of h meters and with an initial upward velocity of u meters/second. The ball's height above ground is given by the equation H(t) = -4.9t2 + vt + h, where H is in meters and t is in seconds. (This is the metric version of the gravity model.)
High-speed elevators function under two limitations: (1) the maximum magnitude of vertical acceleration that a typical human body can experience without discomfort is about 1.2 m/s², and (2) the typical maximum speed attainable is about 8.8 m/s. You board an elevator on a skyscraper's ground floor and are transported 190 m above the ground level in three steps: acceleration of magnitude 1.2 m/s² from rest to 8.8 m/s, followed by constant upward velocity of 8.8 m/s. then deceleration of magnitude 1.2 m/s² from 8.8 m/s to rest. T Part A Determine the elapsed time for each of these 3 stages. Express your answers using two significant figures separated by commas. tace, tconstant, tdec = Submit Part B AFN,acc AFN,constant FN FN Submit Request Answer 2 [5] ΑΣΦ Determine the change in the magnitude of the normal force, expressed as a % of your normal weight during each stage. Express your answers using two significant figures separated by commas. 2 AFN,dec FN Request Answer Part C Complete…
Imagine a diver jumping off a spring board that is 10 feet above the water. The board throws the diver up with an upward velocity of 9 feet per second. That means that if there were no gravity, the diver would keep going up at the rate of 9 feet every second. Fortunately for the diver, there is gravity. Eventually, gravity over comes the force of the diving board and the the diver begins to come down. So over all, the diver is thrown into the air fairly quickly, he slows down until he stops, then begins to come back down (slowly at first, then faster and faster until he hits the water). The height of any object like the diver that is projected into the air can be modeled with the following function: h(t) = -16t^2 + v*t + m In this function: h(t) is the height of the object t seconds after it was thrown into the air. t is the number of seconds after the object was thrown in the air. v is the initial upward velocity (for the diver this was 9 ft per second). m is the initial height of the…
If you walk at 1 km/h down the aisle toward the front of a train that is moving at 60 km/h, what is your speed relative to the ground?
(4D) PLEASE BE CLEAR ON EACH STEP AND IF POSSIBLE GIVE THE ANSWER TYPED IF NOT, BE CLEAR WITH YOUR WRITING, THANKS!

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