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# Velocity

### Wave Propagation in a String of Varying Density

Consider a string of total length L, made up of three segments of equal length. The mass per unit length of the first segment is mu, that of the second is 2mu, and that of the third mu/4. The third segment is tied to a wall, and the string is stretched by a force of magnitude Ts applied to the first segment; Ts is much greater t

### the period of a wave in terms of angular velocity

A). Find an expression for the period of a wave, T, in terms of other kinematic variables. Express your answer in terms of any of f, v, omega, and simple constants such as pi.

### Breaking a Glass Soda Bottle

A glass soda bottle is emptied of soda and filled to the very top with water. A cork is carefully fitted into the top of the bottle, leaving no air between the cork and the water. The top of the bottle has a diameter of D_top = 2.00 cm and the bottom of the bottle has a diameter of D_bot = 6.50 cm. The glass breaks when it is ex

### Torricelli's Theorem

Water stands at a depth H in a large open tank whose side walls are vertical (see attachment for figure). A hole is made in one of the walls at a depth h below the water surface. a) At what distance R from the foot of the wall does the emerging stream strike the floor? Express your answer in terms of the given quantities.

### The Speed of Sound From a Moving Car

Please see the attached document for the question.

### momentum and impulse

Please see attachment. Thank You your help is greatly needed. 1. A stunt person jumps from the roof of a tall building, but no injury occurs because the person lands on a large, air-filled bag. Which one of the following best describes why no injury occurs? 2. Jennifer is walking at 1.63 m/s. If Jennifer weighs 583 N, what

### Velocity and Acceleration using Function and Derivatives

1. The distance-time relationship for a moving object is given by s(t) = kt2 + (6k^2 - 10k)t + 2k, where k is a non-zero constant a) show that acceleration is constant b) Find the time at which the velocity is zero, and determine the position of the object when this occurs. 2. An object moves so that its velocity, v,

### speed of waves on the string

Please see the attached file. The speed of waves on a certain string is 2 m/s. Another string has a mass per unit length that is 4 times as great as the first string and a tension that is 2 times as great. What is the speed of waves on the second string.

### Instantaneous Center of Zero Velocity

See the attached file. The elements of a switching device are shown. If the vertical control rod has a downward velocity of V = 3 ft/sec when phi = 60 degrees, and if roller A is in continuous contact with the horizontal surface determine the magnitude of velocity of C for this instant using the method of "instantaneous cen

### Birefringent Materials Optic Axis

What is meant by the optic axis of a uniaxial birefringent crystal? Could you please describe and explain how birefringent materials may be used to produce linearly and circularly polarized light from unpolarized light? Thank you.

### Motion in two dimensions: Projectile motion.

A ping pong ball falls off a table 1.20 m high at 1.50 m/s. How FAR from the table does the ball hit the floor? What is the speed impact also?

### Projectile motion

Please see the attached file. 1. A rocket is launched at an angle of 53.0° above the horizontal with an initial speed of 100 m/s. The rocket moves for 3.00 s along its initial line of motion with an acceleration of 30.0 m/s2. At this time, its engines fail and the rocket proceeds to move as a projectile. Find (a) the max

### the initial speed of water fired from a squirt gun

A kid fires water horizontally from a squirt gun held 1.6m above the ground. It hits another kid 2.1 m away in the back, at a point of 0.93 m above the ground. what is the initial speed?

### wind velocity

A jetliner with an airspeed of 1000 km/h sets out on a 1500-km flight due south. to maintain a southward direction, however, the plane must be pointed 15 degree west of south. if the flight taks 100 min, what is the wind velocity?

### velocity of the roller coaster

A 350 roller coaster starts from rest at point A and slides down the frictionless loop, which is shown in the accompanying figure (see attachment) How fast is this roller coaster moving at point B? v = ? m/s How hard does it press against the track at point B? F = ? N

### Maxwell velocity distribution for a gas

Please see attached file. 1. For a gas obeying the Maxwell velocity distribution obtain: a) The most probable speed of the particles b) The most probable Kinetic Energy of the particles c) The mean speed of the particles d) The root mean squared speed of the particles the mean kinetic energy of the particles 2. For a

### Flywheel Kinematics

A heavy flywheel is accelerated (rotationally) by a motor that provides constant torque and therefore a constant angular acceleration alpha. The flywheel is assumed to be stationary at time t = 0 in Parts A, B, and C of this problem. a). Find the time t_10 it takes to accelerate the flywheel to 10.0 rps (revolutions per secon

### Spring and Projectile of a thrown ball

A child's toy consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. The spring has a spring constant, k, the ball has a mass, m , and the ramp rises a height, y, above the surface of the table, the surface of which is a height, H, above the ground. Initia

### Physics Problem: Displacement, Velocity and Acceleration

Run a simulation of a ball dropping and measure the displacement, velocity and acceleration. 1. Measure the time that it takes the ball to travel 1 meter, 2 meters, 3 meters and each succeeding meter up to 6 meters for the Earth and the Moon. 2. Graph the distance traveled versus the time for the Earth and the Moon. 3

### Impact of Velocity Reversal

Please include FBD. A 3 kg slider, A, fits loosely in a in the smooth 45 degree slot in the disk shown, which rotates in a Horizontal plane about the center O. If A is held in position by a cord secured to B determine ,T, the tension in the cord fpr a constant rotational velocity of 300 rev./min, around point O in the direct

### Velocity & Displacement of a Block

A spring of constant k=200N/m is attached between a block of mass 2 kg and a vertical wall.The block rests on a frictionless plane and the COG of the block and the spring are in the same line horizontal to the table. If a constant force of 10N (in the positive x direction) is applied to the spring at t=o when the spring in un

### Angular Displacement and Motion

1. The angular displacement of a human centrifuge, of length 30 ft, is given by (theta)= 4[t + 30*e^(-.03t)-30]radians where t is in seconds and and t=0 is start up. If the passenger loses consciousness at an acceleration of 10g's determine the time this would occur. Verify the tangential acceleration is small compared to

### velocity, acceleration, distance motion

Hello I need help with the following Physics problems. 9. A train approaches a small town with a constant velocity of +28.6 m/s. The operator applies the brake, reducing the train's velocity to +11.4 m/s. If the average acceleration of the train during brake is -1.35 m/s^2. For what elapsed time does the operator apply the br

### Determining Magnitude of Velocity and Acceleration

See the attached file for diagram. The fixed horizontal guide carries a pin P whose motion is controlled by the rotating slotted arm OA. If the arm is revolving about O at the constant rate of 2 radians/sec (angular velocity)for the for the interval allowed by the horizontal guide determine the magnitudes of the velocity an

### Simple harmonic motion: Position velocity and period

A raft is bobbing up and down in a lake. Its vertical position x above the flat surface of the water is given by x=0.60sin(3.0t+4.2), where distances are in metres and time t is in seconds. 1. What is the boat's position at t=0? At t=2.8s? 2. What is the period of the raft's oscillation? 3. What is the boat's maximum sp

### Solid mechanics with a positive reference

See attached 1. A 2-lb ball is thrown upward at 30ft/s from an origin 5-ft above the earth's surface. Using for your positive reference a vertical Y axis with its origin at 5ft, DETERMINE FOR THE BALL: a) The maximum height in ft reached b) The elapsed time of flight in seconds until its return to the origin c) Its a

### Velocity of a falling rain drop and air resistance

Please see the attached file for full problem description. Provide solution for Q7 only. Q7. A raindrop is observed at time t=0 when it has mass m and downward velocity u. As it falls under gravity its mass increases by condensation at a constant rate and a resisting force acts on it, proportional to is speed and equal

### Particle Mass and Speed

Please see attached file for full problem description. A particle whose initial mass is m is projected vertically upwards at time t=0 with speed gT, where T is a constant. At time t its speed is u and its mass has increased to me^(t/T). a) If the added mass is at rest when it is acquired, show that d/dt(mue^(t/T)) = -mge^(t

### A rocket is fired vertically upwards with initial speed V and is propelled by ejecting material downwards at a constant rate. To derive the expression for maximum height reached.

(Please refer attachment for detailed problem description) A rocket is fired vertically upwards with initial speed V and is propelled by ejecting material downwards at a constant rate and with a constant speed u relative to the rocket. After a time T the propellant material is exhausted and the rocket still rising. Neglecting

### Equations of motion of a rocket

At time t, the mass of a rocket is M(1-kt), where M and k are constants. At time t, the rocket is moving with speed v vertically upwards near the Earth's surface against constant gravity. Burnt fuel is expelled vertically downwards at speed u relative to the rocket. a) Show that (1-kt)dv/dt = ku-g(1-kt) b) Given that v=0 when