3. A softball player catches a ball of mass m, which is moving towards her with horizontal speed V. While bringing the ball to rest, her hand moved back a distance d. Assuming constant deceleration, the horizontal force exerted on the ball by the hand is (A) mV²/(d) (B) V²m/2d (C) 2mV/d (D) mV/d
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- For a particle of mass "m" moving in a central force field, show that: v²-i²+1²0²-h²[(du/d0)²+u²] 2Starting from rest, a 64.0 kg woman jumps down to the floor from a height of 0.800 m, and immediately jumps back up into the air. While she is in contact with the ground during the time interval 0 < t < 0.800 s, the force she exerts on the floor can be modeled using the function F = 9,200t − 11,500t2 where F is in newtons and t is in seconds. (c) With what speed (in m/s) did she leave it? (Round your answer to at least three significant figures.) (d) To what height (in m) did she jump upon leaving the floor?Suppose you are navigating a spacecraft far from other objects. The mass of the spacecraft is 4.0 104 kg (about 40 tons). The rocket engines are shut off, and you're coasting along with a constant velocity of ‹ 0, 30, 0 › km/s. As you pass the location ‹ 6, 9, 0 › km you briefly fire side thruster rockets, so that your spacecraft experiences a net force of ‹ 5.0 105, 0, 0 › N for 20 s. The ejected gases have a mass that is small compared to the mass of the spacecraft. You then continue coasting with the rocket engines turned off. Where are you an hour later? (Think about what approximations or simplifying assumptions you made in your analysis. Also think about the choice of system: what are the surroundings that exert external forces on your system?)f = m
- A 0.27 kg particle moves in an xy plane according to x(t) = - 11+2 t-6 t³ and y(t) = 17 + 7 t - 9 t², with x and y in meters and t in seconds. At t = 1.0 s, what are (a) the magnitude and (b) the angle (within (-180°, 180°] interval relative to the positive direction of the x axis) of the net force on the particle, and (c) what is the angle of the particle's direction of travel?1. A hose sprays water into a train car. The hose is fixed in place and directed along the tracks, and the train car can move along the tracks without friction. The hose sprays water at a fixed rate a ([a] =MT-1) and speed v; the mass of the empty car is M. If the train car starts empty and at rest at t = 0, what is its speed at time t?An electron with a speed of 1.0 x 10' m/s moves horizontally into a region where a constant vertical force of 4.8 x 10 16 N acts on it. The mass of the electron is 9.11 x 1031 kg. Determine the vertical distance the electron is deflected during the time it has moved 42 mm horizontally.
- A stationary 2.17-kg object is struck by a stick. The object experiences a horizontal force given by F = at - bt 2, where t is the time in seconds from the instant the stick first contacts the object. If a = 1,500,000 N/s and b = 20,000,000 N/s?, what is the speed of the object just after it comes away from the stick at t = 2.55 x 103 s? %3DA freight train consists of two 8.00×104 kg5.60×104 kg engines and 45 cars with average masses of 5.50×104 kg5.50×104 kg. (a) What force must each engine exert backward on the track to accelerate the train at a rate of 4.00×10−2 m/s if the force of friction is 6.20×105 N, assuming the engines exert identical forces? This is not a large frictional force for such a massive system. Rolling friction for trains is small, and consequently trains are very energy-efficient transportation systems. (b) What is the force in the coupling between the 37th and 38th cars (this is the force each exerts on the other), assuming all cars have the same mass and that friction is evenly distributed among all of the cars and engines?Help