Assume the resistive force acting on a speed skater is proportional to the square of the skater’s speed v and is given by f = −kmv2, where k is a constant and m is the skater’s mass. The skater crosses the finish line of a straight-line race with speed vi and then slows down by coasting on his skates. Show that the skater’s speed at any time t after crossing the finish line is v(t) = vi/(1 + ktvi).
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Physics for Scientists and Engineers with Modern Physics
Additional Science Textbook Solutions
Conceptual Physics (12th Edition)
The Physics of Everyday Phenomena
Lecture- Tutorials for Introductory Astronomy
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
Physics for Scientists and Engineers, Technology Update (No access codes included)
Sears And Zemansky's University Physics With Modern Physics
- A rope, attached to a weight, goes up through a pulley at the ceiling and back down to a worker. The worker holds the rope at the same height as the connection point between the rope and weight. The distance from the connection point to the ceiling is 30 ft. Suppose the worker stands directly next to the weight (.e., a total rope length of 60 ft) and begins to walk away at a constant rate of 2 ft/s. How fast is the weight rising when the worker has walked: 10 feet? Answer= 30 feet? Answerarrow_forwardA speedboat weighing 644 lbs is powered by a constant force of 40 lbs. Friction between the boat and the water is negligible, but there is wind resistance proportional to the velocity of the boat and is 10 lbs. for a speed of 5 fps. Assuming the boat started from rest, find the speed after 10 sec.arrow_forwardProblem 1: A nurse pushes a patient’s bed with a constant force of 30 N. If the bed has a mass of 100 kg and was initially at rest, how fast is the bed moving after 5 seconds? Problem 2: A young man was rushed to the operating room to treat several gunshot wounds. If a rib fracture requires a force of 3,200 N, does a bullet with a mass of 7.5 grams that strikes the rib with an deacceleration of 4.4x105 m/s2 have enough force to create the fracture? What is the force?arrow_forward
- Three youths push a 40.0-kg block of ice so that it begins to coast on a frozen lake. With an initial speed Vi of 3.00 m/s, the block of ice now moves up an icy ramp at the edge of the lake. Neglecting air resistance and in the absence of any friction between the ice block and the frozen lake and ramp, use the CMEP to calculate how high up the ramp (h in the figure) the block of ice moves before stopping. As a suggestion, use the base of the ramp as GZ. 0.204 m 0.625 m 0.459 m 0.511 m 0.165 m 0.270 m O O Oarrow_forwardA 3 kg particle starts from rest and moves a distance of 4 m in 2 sec under the action of a single constant force. find the magnitude of the forcearrow_forwardA rope, attached to a weight, goes up through a pulley at the ceiling and back down to a worker. The worker holds the rope at the same height as the connection point between the rope and weight.The distance from the connection point to the ceiling is 35 feet.Suppose the worker stands directly next to the weight (i.e., a total rope length of 70 feet) and begins to walk away at a constant rate of 3 ft/s. How fast is the weight rising when the worker has walked a)10 feet? b)30 feet?arrow_forward
- For t < 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed v,. Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed: Fnet - - mkv? î, where k is a constant. The speed of the object after t = 0 is given by v = v;/(1 + kv,t). (a) Find the position x of the object as a function of time. (b) Find the object's velocity as a function of position.arrow_forwardSuppose a rocket is at an elevation of 100 km and has an initial velocity of 1.00 x 10^4 m/s directed vertically upward. If the rocket engines do not burn and no other force other than earth's gravity acts on the rocket, how far does it go?arrow_forwardThe only force acting on an object of mass 2.00 kg moving along the x-axis is shown in the figure. If the speed vx is +2.0 m / s at t = 0, what is the speed at t = 4.0 s?arrow_forward
- An object of a mass of 2.5-kg is launched upwards, with an initial speed of 39 m/s. How fast is the object traveling after falling back to its original launch height? Assume that there is no air resistance.arrow_forwardA rope, attached to a weight, goes up through a pulley at the ceiling and back down to a worker. The worker holds the rope at the same height the connection point between the rope and weight. The distance from the connection point to the ceiling is 45 ft. Suppose the worker stands directly next to the weight (i.e., a total rope length of 90 ft) and begins to walk away at a constant rate of 4 ft/s. How fast is the weight rising when the worker has walked: 10 feet? Answer= 30 feet? Answer=arrow_forwardImagine a skydiver with a mass of m jumping out of an airplane at an altitude of h. As the skydiver descends, they experience two forces: air resistance and gravity. The force of air resistance varies with time and is described by the following function, where t is the time in seconds since t e skydiver has jumped: vec 2 (F)(t) = (0.5t)ha (x) + (0.11 +0.3t)hat(y) a) Create a air free body diagrar for the skydiver at t = 2 seconds. b) - What is the net for e acting on the skydiver at t = 2 seconds? c) What i the magnitude of the acceleration of the skydiver at t = 2 seconds? Imagine a skydiver with a mass of m jumping out of an airplane at an altitude of h. As the skydiver descends, they experience two forces: air resistance and gravity. The force of air resistance varies with time and is described by the following function, where t is the time in seconds since the skydiver has jumped: Fair (t) = (0.5t)2 + (0.12 + 0.3t)ŷ a) Create a free-body diagram for the skydiver at t = 2 seconds.…arrow_forward
- Glencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning