A child of mass m starts from rest and slides with- out friction from a height h along a curved waterslide (Fig. P5.46). She is launched from a height h/5 into the pool. (a) Is mechanical energy conserved? Why? (b) Give the gravi- tational potential energy associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands in the pool. (c) Determine her initial speed h at the launch point in terms of g and h. (d) Determine her maximum airborne height ymax in terms of h, g, and the hori- zontal speed at that height, w (e) Use the x-component of the answer to part (c) to eliminate y from the answer to part (d), giving the height ymax in terms of g, h, and the launch angle 0. (f) Would your answers be the same if the waterslide were not frictionless? Explain. Утах th/5 Figure P5.46

A child of mass m starts from rest and slides with- out friction from a height h along a curved waterslide (Fig. P5.46). She is launched from a height h/5 into the pool. (a) Is mechanical energy conserved? Why? (b) Give the gravi- tational potential energy associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands in the pool. (c) Determine her initial speed h at the launch point in terms of g and h. (d) Determine her maximum airborne height ymax in terms of h, g, and the hori- zontal speed at that height, w (e) Use the x-component of the answer to part (c) to eliminate y from the answer to part (d), giving the height ymax in terms of g, h, and the launch angle 0. (f) Would your answers be the same if the waterslide were not frictionless? Explain. Утах th/5 Figure P5.46

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)...

See similar textbooks

Similar questions

A roller coaster design is presented to you where the maximum speed of the car will be 9.00 meters per second and the highest point of the tracks is 5.099 meters above the lowest point. Do you accept or reject the design? Use conservation of energy to justify your decision.
A 79 kg bike racer climbs a 1100m long section of road that has a slope of 4.3∘. By how much does his gravitational potential energy change during this climb? Express your answer with the appropriate units
Please answer it within 30 minutes.I will upvote!
A child of mass m starts from rest and slides without friction from a height h along a curved waterslide (Fig. P5.46). She is launched from a height h/5 into the pool. (a) Is mechanical energy conserved? Why? (b) Give the gravitational potential energy associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands inthe pool. (c) Determine her initial speed V0 at the launch point in terms of g and h. (d) Determine her maximum airborne height ymaxin terms of h, g, and the horizontal speed at that height, v0x. (e) Use the x-component of the answer to part (c) to eliminate from theanswer to part (d), giving the height ymax in terms of g, h, and the launch angle θ. (f) Would your answers be the same if the waterslide were not frictionless? Explain.
Computation. A ceramic figurine is launched at 31 m/s at 34.2° above horizontal. What is its speed when it reaches half its maximum height? [Hint: Start by obtaining the relation between its launch velocity (speed and angle) and its maximum height. Use that relation to eliminate the final height from the energy conservation equation.] v= m/s Record your numerical answer below, assuming three significant figures. Remember to include a "-" if/when necessary. ☆
Given: A shooting guard throws a basketball m = 1 kg straight up with an initial speed of v0 = 5.5 m/s. He releases the ball at shoulder height h0 = 1.95 m. Let gravitational potential energy be zero at ground level. Give the total mechanical energy of the ball E in terms of maximum height hm it reaches, the mass m, and the gravitational acceleration g. What is the height, hm in meters?
Q ) What is the total mechanical energy of falling baseball from the highest of 4 m, 3.22 m and 2.25 m? For more informal, weight of the baseball is 0.3 kg and the gravity is 10 m's.
In a downhill ski race surprisingly little advantage is gained by getting a running start. This is because the initial kinetic energy is small compared with the gain in gravitational potential energy even on small hills. To demonstrate this, find the final speed and the time taken for a skier who skies 60.0 m along a 25° slope neglecting friction for the following two cases. (Note that this time difference can be very significant in competitive events so it is still worthwhile to get a running start.) (a) starting from rest_____ final speed m/s_____ time taken s(b) starting with an initial speed of 2.50 m/s_____ final speed m/s_____ time taken s
An Olympic swimmer stands on top of a platform at a height H above a swimming pool. At the moment of jumping into the pool, he jumps with a speed v_0 forming an angle θ with the horizontal, just as shown in the figure. The swimmer reaches a maximum height h measured from the platform to point B. (a) Using the conservation of energy, show that the height h is given by
You design a roller coaster with a 57 m starting hill. Not taking friction into account, what is the maximum speed of a roller coaster cart at the bottom of this hill?
A box is given a push across a horizontal surface. The box has a mass m, the push gives it an initial speed of V₁, and the coefficient of kinetic friction between the box and the surface is Mk. (a) Use energy considerations to find an expression for the distance the box moves before it stops. (Use any variable or symbol stated above along with the following as necessary: g.) d = 2μ8 (b) What If? If the initial speed of the box is increased by a factor of 4, determine an expression for the new distance dnew the box slides in terms of the old distance d. d