A child of mass m = 25 kg starts from rest and slides without friction from a height h along a slide next to a pool. She is launched from a height into the air over the pool. (a) Using conservation of energy, find the speed of the child at the end of the slide. (b) Using your result of part (a) anợ eguations related to a projectile, find ymax as shown in the picture, in terms of h and 6. Imax
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- A large cruise ship of mass 6.30 x 107 kg has a speed of 11.8 m/s at some instant. (a) What is the ship's kinetic energy at this time? (b) How much work is required to stop it? (Give the work done on the ship. Include the sign of the value in your answer.) (c) What is the magnitude of the constant force required to stop it as it undergoes a displacement of 3.90 km?A 56.0-kg runner has a speed of 4.10 m/s at one instant during a long-distance event. (a) What is the runner's kinetic energy at this instant? (b) If he doubles his speed to reach the finish line, by what factor does his kinetic energy change? KE KE, Additional Materials еВookA skateboarder is at the top of a frictionless ramp defined by the function y = z². The top of the ramp is located at (-5m, 25m), and the skateboarder skates to the bottom of the ramp, (0m, 0m). (a) What nonconservative forces are in this problem? (b) What is the total nonconservative work done? (c) Is mechanical energy conserved? (d) What is the skateboarder's speed at the bottom of the ramp?
- A construction worker’s hard hat is rated at 100 J, meaning that it can protect the wearer from an impact not exceeding that energy. (a) What is the speed of a 2 kg tile having that amount of kinetic energy? (b) What is the maximum height from which that tile could fall and strike the hat without injuring the wearer?A large cruise ship of mass 6.70 ✕ 107 kg has a speed of 10.4 m/s at some instant. (a) What is the ship's kinetic energy at this time? J(b) How much work is required to stop it? (Give the work done on the ship. Include the sign of the value in your answer.) J(c) What is the magnitude of the constant force required to stop it as it undergoes a displacement of 2.70 km?Consider the skateboarder in the Figure. If she has a mass of 55 kg, an initial velocity of 20 m/s, and a velocity of 12 m/s at the top of the ramp along horizontal direction. After that she flies into the air and strikes the ground. (Ignore air friction and the kinetic energy of the skateboard) a)What is the work done by friction on the skateboarder? (b)Calculate the flight time of the skateboarder. (c)Calculate the velocity at which she strikes at the
- A 65.1 kg runner has a speed of 4.70 m/s at one instant during a long-distance event. (a) What is the runner's kinetic energy at this instant (in J)? J (b) How much net work (in J) is required to triple her speed?A large cruise ship of mass 7.00 ✕ 107 kg has a speed of 12.2 m/s at some instant. (a) What is the ship's kinetic energy at this time? J(b) How much work is required to stop it? (Give the work done on the ship. Include the sign of the value in your answer.) J(c) What is the magnitude of the constant force required to stop it as it undergoes a displacement of 3.00 km? NA student pulls a 2.54 kg box from rest 3.80 m on a flat surface by a rope. (a) What is the work done on the box, if the change is momentum is 4.44 ? (b) If the student pulls the rope for 2.00 seconds, what is the angle the rope makes the surface?
- The figure here shows a plot of potential energy U versus position x of a 0.878 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) Three values are UA-15.0J, U₂ - 35.0J and U-45.0 J. The particle is released atx -4.50 m with an initial speed of 7.99 m/s, headed in the negative x direction. (a) If the particle can reach x - 1.00 m, what is its speed there, and if it cannot, what is its turning point? What are the (b) magnitude and (c) direction of the force on the particle as it begins to move to the left of x-4.00 m? Suppose, instead, the particle is headed in the positive x direction when it is released at x -4.50 m at speed 7.99 m/s. (d) If the particle can reach x - 7.00 m, what is its speed there, and if it cannot, what is its turning point? What are the (e) magnitude and (f) direction of the force on the particle as it begins to move to the right of x-5.00 m? U(J) Uc UB UA 2 4 x (m) 6For a certain run, the following data is obtained when filling up Table 2 of the manual: Mass of cart = 600 g, hanging mass = 33 g, distance travelled by the cart = 49 cm, initial speed of the cart = 0.38 m/s, Final speed of the cart = 0.8 m/s, Calculate the percent difference between change in potential energy and change in Kinetic Energy.A large cruise ship of mass 6.00 ✕ 107 kg has a speed of 12.4 m/s at some instant. (a) What is the ship's kinetic energy at this time? J(b) How much work is required to stop it? (Give the work done on the ship. Include the sign of the value in your answer.) J(c) What is the magnitude of the constant force required to stop it as it undergoes a displacement of 3.40 km? N