Existence and Uniqueness Theorem. A motorboat of total mass m = 200kg is facing the shoreline and drifting away at 0.5 m/s. In order to return to shore you apply a constant force of 100 Newtons in the direction of the shore. However, the boat is also subject to a drag force of 400v² where v is the velocity in m/s. (a) Find the ODE satisfied by v(t), the velocity in the direction away from the shore, where t is measured in seconds. (b) Find v(t). (c) How many seconds pass before the boat starts heading toward the shore?

Existence and Uniqueness Theorem. A motorboat of total mass m = 200kg is facing the shoreline and drifting away at 0.5 m/s. In order to return to shore you apply a constant force of 100 Newtons in the direction of the shore. However, the boat is also subject to a drag force of 400v² where v is the velocity in m/s. (a) Find the ODE satisfied by v(t), the velocity in the direction away from the shore, where t is measured in seconds. (b) Find v(t). (c) How many seconds pass before the boat starts heading toward the shore?

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 warehouse worker is pushing a 90.0 kg crate with a horizontal force of 276N at a speed of v = 0.875m/s across the warehouse floor. He encounters a rough horizontal section of the floor that is 0.75 m long and where the coefficient of kinetic friction between the crate and floor is 0.353. (a) Determine the magnitude and direction of the net force acting on the crate while it is pushed over the rough section of the floor. magnitude Ndirection ---Select--- up down in the same direction as the motion of the crate in the opposite direction as the motion of the crate (b) Determine the net work done on the crate while it is pushed over the rough section of the floor. J (c) Find the speed of the crate when it reaches the end of the rough surface. m/s
The force on a particle of mass 2.0 kg varies with position according to F(x) = −3.0x2 (x in meters, F(x) in newtons). The particle's speed at x = 3.0 m is 5.5 m/s. Find the particle's speed (in m/s) at x = 2.0 m, using the origin as the reference point. Find the particle's speed (in m/s) at = 2.0 m, using x = 5.0 mas the reference point.
A toy rocket engine is securely fastened to a large puck that can glide with negligible friction over a horizontal surface, taken as the xy plane. The 4.80-kg puck has a velocity of 1.201 m/s at one instant. Eight seconds later, its velocity is (6.001 + 8.0ĵ) m/s. (a) Assuming the rocket engine exerts a constant horizontal force, find the components of the force. We know the change in velocity during an 8 second time interval. How do you calculate the acceleration?Î + Work with x and y components separately.ĵ) N (b) Find its magnitude. X You appear to have correctly calculated the magnitude using your incorrect values from part (a). N X
An object of mass m = 2.9 kg is free to move on a horizontal surface without any friction. It is initially at rest and starts moving under a net force of F = (3N)i + (4N)j. What is the object's speed in m/s after moving 1 meter?
The only force acting on a 4.5 kg body as it moves along the positive x axis has an x component Fx = -6x N, where x is in meters. The velocity of the body at x = 1.9 m is 8.2 m/s. (a) What is the velocity of the body at x = 4.5 m? (b) At what positive value of x will the body have a velocity of 5.9 m/s?
= -3x N, where x is in meters. The velocity of the body at The only force acting on a 3.8 kg body as it moves along the positive x axis has an x component Fx x = 2.5 m is 11 m/s. (a) What is the velocity of the body at x = 4.2 m? (b) At what positive value of x will the body have a velocity of 3.4 m/s? (a) Number Units (b) Number Units
The only force acting on a 3.6 kg body as it moves along the positive x axis has an x component Fx = -7x N, where x is in meters. The velocity of the body at x = 2.2 m is 11 m/s. (a) What is the velocity of the body at x = 4.6 m? (b) At what positive value of x will the body have a velocity of 3.4 m/s? (a) Number Units (b) Number Units
A man pushing a crate of mass m = 92.0 kg at a speed of v = 0.870 m/s encounters a rough horizontal surface of length = 0.65 m as in the figure below. If the coefficient of kinetic friction between the crate and rough surface is 0.350 and he exerts a constant horizontal force of 279 N on the crate. (a) Find the magnitude and direction of the net force on the crate while it is on the rough surface. magnitude N direction ---Select--- (b) Find the net work done on the crate while it is on the rough surface. (c) Find the speed of the crate when it reaches the end of the rough surface. m/s
The only force acting on a 3.6 kg body as it moves along the positive x axis has an x component Fx = - 5x N, where x is in meters. The velocity of the body at x = 1.8 m is 9.0 m/s. (a) What is the velocity of the body at x = 4.1 m? (b) At what positive value of x will the body have a velocity of 2.5 m/s?
Here we have a block of mass (m=2.50kg) resting on a place inclined at an angle of ø=30° to the horizontal. The coefficient of static friction between the block and the plane is Ustatic = 0.135 and the block is stationary but just on the point of sliding up the slope. The diagram shows the four forces acting on the block: an applied force F1 acting up the slope, the block's weight mg, the normal reaction force N and the force of static friction, Ff. In this case, the force of static friction acts down the slope, opposing the tendency of the block to move up the slope. Find the the maximum magnitude of the applied force F1 that can be exerted if the block is to remain stationary.
A man (mass 45 kg) shoots himself out of a cannon straight upward with an initial velocity of 46 m/s towards a ledge 95 m above the cannon. There’s some air resistance occurring, and the man’s upward trajectory ends 6.0 meters below the ledge. A) What was the average force of frictional air resistance the man experienced during his upward motion? B) Assuming the same average air resistance on the way down, how fast will the man’s impact velocity be when he returns to the “ground” level of the cannon’s muzzle? Please answer the question on paper. I do not understand when it is typed out. Thank you
A 547g squirrel with a frontal surface area of 0.0145m2 falls to the ground from a 5.3m tree. Assume the density of air is 1.21kg/m3. Neglecting the drag force, what is the velocity, in meters per second, of a 56kg person after falling, from rest, by that same distance?