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# Velocity

### Maximum velocity of a mass on a spring vibrating up and down

Suppose a mass on a spring is vibrating up and down with amplitude of 5.0 cm and a frequency of 0.80 Hz. (A) What is the angular speed w of the system? (B) Describe the motion of the mass in the form y = A sin (wt) (In other words, put in the values for A and w) (C) What is the maximum velocity of the mass, and

### Approximate the velocity

A quarterback on a football team throws a pass, releasing the ball at an angle of 30 degree with the horizontal. Approximate the velocity at which the football must be released to reach a receiver 150 feet downfield (disregard air resistance)

### Frictional Force and Velocity of Water

A 150-lb fireman is holding a hose which has a nozzle diameter of 1 inch and hose diameter of 2 inches. If the velocity of the water at discharge is 60 ft/s - determine the resultant normal and frictional force acting on the man's feet at the ground. (Neglect the weight of the hose and the water within it. yw = 62.4 lb/ft3).

### 7 problems on rotational motion and two problems on density

1. Competitive divers pull their limbs in a curl up their bodies when they do flips. Just before entering the water, they fully extend their limbs to enter straight down. Explain the effect of both actions on their angular velocity. What is the effect of these actions on their angular momentum? 2. (A) Show that for a hoop of

### Projectile Motion and Horizontal Projection

A mountain climber jumps a 1.6 m wide crevasse by leaping horizontally with a speed of 7.0 m/s. (a) If the climber's direction of motion on landing is -45°, what is the height difference between the two sides of the crevasse? (b) Where does the climber land?

### Kinetic energy compared

Compared to a car moving at 10 miles per hour, how much kinetic energy does that same car have when it moves at 20 miles per hour? At 30 miles per hour? At 60 miles per hour? What do these numbers suggest to you about the difficulty of stopping a car as its speed increases?

### Derivatives : Displacement, Velocity and Acceleration

A car brakes in an emergency, the moment the brakes are first applied is t=0. the car's distance, s, from the point at which the brakes were first applied is given by: S = -0.1t^3 + 20t + 0.1 (i) Differentiate s to find formulae for the velocity and acceleration. (ii) Find the time at which the car comes to a stop. (iii)

### Force on Current Carrying Wires and Drift Velocity

Please see the attached file for the problem statement, and provide a fully worked-out solution. In order to get an idea of the magnitude of magnetic forces, find the force per unit length between very long equal and opposite 10 ampere currents separated by 1 centimeter. Find the ratio of this to the weight per unit length of

### Two dimensional motion

A baseball leaves a pitcher's hand with an unknown horizontal initial velocity (Vo). The ball lands in the catcher's mitt a distance of 18.5 meters away. If the point of release is one meter above the catcher's mitt, what is the the initial velocity of the ball?

### Centre of Mass: Cart and Spring

The figure shows a cart and spring. The mass of the cart is presently unknown. However, the solution of the equations of motion of the center of mass is (see attachment). If the spring constant is 503 N/m what is the mass of the cart? Also calculate the location of the center of mass at t = 0.23 seconds, and the velocity of the

### Electron drift velocity

Calculate the drift velocity of electrons in a copper wire given the current flowing in it, its diameter and density. A copper wire 2.5 millimeters in diameter is carrying a current of 10 amperes. Assume one free electron per copper atom and find the magnitude of the drift velocity. [Copper has a density of 8.92 grams/(cent

### Physics - Motion

A .51kg object is at rest. a 2.70 N force to the right acts on the object during a time interval of 1.32s A) what is the velocity of the object at the end of this time interval? (in m/s) B) at the end of this interval, a constant force of 3.86N to the left is applied for 3.02s What is the velocity at the end of the 3.02s?

### Absolute and Gauge Pressure

A dam to create a large fresh water lake is constructed. It will be approximately 14 meters deep. A horizontal pipe 1.2 meters long and 4 cm in diameter will pass through the dam at a depth of 7 meters to allow for release of the water in emergencies and for sampling. In normal situations, a plug will secure the pipe opening.

### Collision: Loss of Energy

Train A (mass = 400kg) successfully couples with a Train (mass=600 kg). Train A is moving at 2.5 m/s before the collision, and Train B is initially at rest. What is the final velocity of the coupled trains? What is the initial kinetic energy? What is the final kinetic energy? How much kinetic energy is lost? What fraction of the

### Kinematics of a Plane

A plane initially flying at 120 m/s [E] accelerates at 5.6 m/s^2[W] for 20.0 s. a)What is plane's final velocity? b) What is plane's displacement in this time? A bullet leaves the muzzle of a gun with a velocity of 410m/s. The length of the gun barrel is 0.50m. a) What is average velocity of the bullet inside the barrel of

### Physsics - Modern Physics

Could you help me? A ball is thrown vertically upwards with an initial speed of 40m/s a) What is the value of the instantaneous speed and the acceleration when the ball reaches its maximum height? b) How long does it take to reach this height? c) How long does it take the ball to fall from the maximum height to the o

### The dispersion relation

The dispersion relation for the longitudinal oscillations of a one-dimensional chain of N identical masses m connected by springs with elastic constant C is given by: w(k) = 2(C/m)^1/2|sin(ka/2)| where a is the equilibrium separation of the masses. (a) Show that the mode with wavevector k + 2pi/a has the same pattern

### phase velocity and group velocity of the deep water wave

Please see the attached file for full problem description. For deep water waves the angular frequency is related to the angular wave number by the following relation: w^2 = gk g=9.8 m/s2 Such a relationship is called a dispersion relation. a) Use the fact that the Phase Velocity is defined as v_p = w/k to sho

### expressions of the velocity and acceleration vectors

Please see the attached file. 22. For the case of plane polar coordinate r, theta, write the unit vectors and e_theta in terms of i and j. Hence show that and. By starting with r = re_r, and differentiating, rederive the expressions for the components of the velocity and acceleration vectors.

### Coefficient of Static Friction Between Coin and Turntable

A coin is placed 10.0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached, at which point the coin slides off. What is the coefficient of static friction between the coin and the turntable?

### Horizontal Component of a Balls Velocity and Time in Air

A second baseman tossed a ball to the first baseman, who catches it at the same level from which it was thrown. The throw had an initial speed of 15.0m/s with an angle of 39.0 above the horizontal. a) What is the horizontal of the component of the ball's velocity just before it is caught? b) How long is the ball in the air

### Physics - Speed and Velocity

In a local bar, a customer slides an empty beer mug down the counter for a refill. The bartender is momentarily distracted and does not see the mug, which slides off the counter and strikes the floor at distance d from the base of the counter. The height of the counter is h. (a) With what speed did the mug leave the counter?

### Ideal Ball Projectile Motion

A ball is thrown directly downward, with an initial speed of 8.50 m/s, from a height of 31.0 m. After what time interval does the ball strike the ground?

### Toy Cars: Velocity, position, and acceleration

At t = 0, one toy car is set rolling on a straight track with initial position 13.0 cm, initial velocity -3.5 cm/s, and constant acceleration 2.50 cm/(s^2). At the same moment, another toy car is set rolling on an adjacent track with initial position 10.5 cm, an initial velocity of 6.10 cm/s, and constant zero acceleration. (a)

### 4 Problems: Vectors, Displacement and equations of motion.

Please see the attached file for full problem description. 1.) A basketball player runs down the court, following the path indicated by the vectors A, B, and C in Figure 3-38. The magnitudes of these three vectors are: A = 10.0 m, B = 21.0 m, and C = 7.0 m. Let the +x axis point to the right and the +y axis point to the far s

### The wavelength and phase speed of microwaves

Determine the wavelength and phase speed of microwaves of frequency 2.45GHz (i) in a vacuum, (ii) in two different plasmas in which there is a uniform distribution of electrons with different number density.

### Child's speed

A child in an airport is able to cover 348 meters in 4 minutes running at a steady speed down a moving sidewalk in the direction of the sidewalks motion. Running a the same speed in the direction opposite to the sidewalks movement, the child is able to cover 275 meters in 5 minutes. What is the child's running speed on a still s

### Physics - Pressure and Volume

1. Calculate the following. a. 100 ml of liquid A has a mass of 250 g. What is its density, in kg/L? (Note: 1 L = 1000 ml = 0.001 m3) b. Liquid B has a specific gravity of 0.98. How much does 1 L weigh, in an Earth-standard gravitational field? 2. The pipe shown above expands from an internal diameter of 3 cm to an

### Projectile Motion: Projected from hight h horizontally

A ball projected horizontally from a height of 50 ft. hits ground at a distance of 100 ft measured from the foot of the vertical structure. Find the velocity of projection.

### A) A projectile is fired straight up at a speed of v0 at a latitude of (alpha) degrees. Show that in the time the projectile is airborne, it is deflected a distance of 4 v0*3 cos(alpha)/3 g^2 to the west. c) Show that for objects confined to land or for objects in which their net vertical acceleration is small in the inertial reference frame, such as storm systems, the maximum magnitude of the Coriolis force is at the north pole with a maximum magnitude of 2m* (Omega0)* v0, where v0 is the object's speed in the east-north direction, or another words along the ground. Thus, show even for fast moving objects with speeds of say 100 m/s, the ratio of the Coriolis acceleration=to that of g is approximately 0.15 percent.

A) A projectile is fired straight up at a speed of v0 at a latitude of (alpha) degrees. Show that in the time the projectile is airborne, it is deflected a distance of 4 v0*3 cos(alpha)/3 g^2 to the west. c) Show that for objects confined to land or for objects in which their net vertical acceleration is small in the inertia