An experimental rail car with a rocket mounted on it is free to slide on a rail that is so slippery it can be considered to be frictionless.  The force that the rocket exerts on the car is given by: F(x)=  Ax2N, 0396m       where x is the position along the rail and A = 18.5.  The mass of the rail car is 6390 kg.  The rail car starts from rest. (a) What are the units of A? (b) What is the total work done on the rail car by the rocket in the first 448 m of travel? (answer: 4.98 x 107 J) (c) What is the speed of the rail car after the first 448 m of travel? (answer: 125 m/s)

G=25

Tarzan, who weighs 777 N, swings from a cliff at the end of a 16.5 m vine that hangs from a high tree limb and initially makes an angle of 21.9° with the vertical. Assume that an x axis points horizontally away from the cliff edge and a y axis extends upward. Immediately after Tarzan steps off the cliff, the tension in the vine is 721 N. Just then, what are (a) the force from the vine on Tarzan in unit-vector notation, and (b) the net force acting on Tarzan in unit-vector notation? What are (c) the magnitude and (d) the direction (measured counterclockwise from the positive x-axis) of the net force acting on Tarzan? What are (e) the magnitude and (f) the direction of Tarzan's acceleration just then?

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 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.…

A ball with mass 0.75 kg is thrown upward with initial velocity 25 m/s from the roof of a building 20 m high. Assume there is a force due to |v| air resistance of magnitude directed opposite to the velocity, where 30 the velocity v is measured in m/s. NOTE: Use g=9.8 m/s² as the acceleration due to gravity. Round your answers to 2 decimal places. a) Find the maximum height above the ground that the ball reaches. Height: 51.89 m Time: 5.81 X b) Find the time that the ball hits the ground. seconds X c) Use a graphing utility to plot the graphs of velocity and position versus time. Edit

A parachutist whose mass is 90 kg drops from a helicopter hovering 1500 m above the ground and falls toward the ground under the influence of gravity. Assume that the force due to air resistance is proportional to the velocity of the parachutist, with the proportionality constant b₁ = 20 N-sec/m when the chute is closed and b₂ = 100 N-sec/m when the chute is open. If the chute does not open until the velocity of the parachutist reaches 35 m/sec, after how many seconds will the parachutist reach the ground? Assume that the acceleration due to gravity is 9.81 m/sec². The parachutist will reach the ground after (Round to two decimal places as needed.) seconds.

An electron is a subatomic particle (m = 9.11 x 10-31 kg) that is subject to electric forces. An electron moving in the +x direction accelerates from an initial velocity of +6.88 x 105 m/s to a final velocity of 2.30 x 106 m/s while traveling a distance of 0.0685 m. The electron's acceleration is due to two electric forces parallel to the x axis: F₁ = 7.84 x 10-17 N, and F2, which points in the -x direction. Find the magnitudes of (a) the net force acting on the electron and (b) the electric force F2. F₂ F₁ VO (a) Number i ! Units N (b) Number Units N eTextbook and Media -> C Σ > F2 F₁ וום 1 0> Assistance Used

An constant applied force of 40.1 N lifts an 2.50 kg mass straight up, resulting in a final speed of 3.6 m/s. What distance did the mass move if it was initially at rest?

A mysterious force acts on all particles along a particular line and always points towards a particular point P on the line. The magnitude of the force on a particle increases as the cube of the distance from that point, that is, F∝ r3, if the distance from the P to the position of the particle is r. It has been determined that the constant of proportionality is 0.23 N/m3, i.e. the magnitude of the force on a particle can be written as 0.23r3, when the particle is at a distance r from the force center. Find the magnitude of the potential energy, in joules, of a particle subjected to this force when the particle is at a distance 0.21 m from point P assuming the potential energy to be zero when the particle is at P.  PE= ?

A bowling ball weighing 54.0 N initially moves at a speed of 5.60 m/s. How long must a force of 36.0 N be applied to the ball to stop it?