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# Velocity

### Block-Bullet System

A 3.16 kg block of wood rests on the muzzle opening of a vertically oriented rifle, the stock of the rifle being firmly planted on the ground. When the rifle is fired, an 8.10 g bullet (velocity = 850 m/s, straight upward) becomes completely embedded in the block. (a) Using the conservation of linear momentum, find the velocity

### Find the velocity with which the projectile exits from the block.

1) A 0.170 kg projectile (bullet) is fired with a velocity of +720 m/s at a 2.00 kg wooden block that rests on a frictionless table. The velocity of the block, immediately after the projectile passes through it, is +40.0 m/s. Find the velocity with which the projectile exits from the block. 2) A two-stage rocket moves in spac

### Method of Subsitution: Velocity from Displacement & Acceleration

In science, we calculate the displacement of an object (how far it travels) and the velocity of an object (how fast it is moving) using the displacement equation and the velocity equation. where x is the displacement of the object, measured in meters t is the amount of time that we analyze the movement of the object, measu

### Calculating time to land

If a steel I-beam falls from the top of a 96 foot high building, how long before it hits the ground? (if an object is given an initial velocity v feet per second from a height of S feet it's height after t seconds is given by: S = -16t^2 + vt + s)

### Momentum of a Particle

The momentum of a particle is proportional to the square of its velocity. True or false? Please also explain why.

### Distance travelled

A car travels along a straight road, heading West for 3 hours, and then travels NE on another road for 2 hours. If the car has maintained a constant speed of 55 mi/hr, how far is it from its starting point?

### Turbomachinery: Impulse & Reaction Turbines

Question 4: An impulse air turbine has a total (on static) inlet pressure and temperature of 11,25 bar, 600 degrees K and exhausts to the atmosphere at 0.91 bar. The nozzle efficiency is 87% and its exit angle is 71 degrees. The rotor efficiency is 65%. If the blade speed if 190 m/s at the mean radius of 12cm, calculate the powe

### Angular Speed and Velocity

A merry-go-round makes 24 revolutions in a 3.0-min ride. (a) What is it's average angular speed in rad/s? (b) What are the tangential speed of two people 4.0 m and 5.0 m from the center, or axis of rotation?

### Features of a "stability loop" in a jet engine combustor

A "stability loop" of a combustor is a diagram showing equivalence ratio versus air mass flow conditions provided to the combustor. Sketch and explain the features of the stability loop.

### Determine the Thermal Efficiency

An aircraft is flying at true airspeed of 270m/s, each jet engine producing 10,000 lb max thrust for a fuel flow of 0.3 kg/s. Noting that the lower calorific value of AVTUR (Jetfuel) is 42 MJ/kg, determine the engine's overall thermal efficiency in this operating condition.

### Linear Momentum and Collisions

Two spheres collide on a horizontal frictionless surface. The first sphere has mass 1.0 kg is initially moving at 3.0 m/sec, the second sphere has mass 2.0 kg is intially at rest. Show the algebraic steps what is the velocity of the first sphere after the collision? a) if there was an elastic collision b) if there was an

### Solving for Harmonic Motion

Question: A body oscillates with simple harmonic motion along the x-axis. Its displacement varies with time according to the equation x=5(pi/t +pi/3). The velocity (in m/s) of the body at t=1 second is equal to what value?

### Centripetal force: Force exerted by the rope

A 50 kg ice skater is moving at 5m/s when she grabs the loose end of the rope,the opposite end of which is tied to a pole.She then moves in a circle of radius 1M around the pole.What is the force exerted by the rope on her arms? I think F=M*V^2/r =250N am I right?

### Rate of Change of Volume and Diameter of a Tree, Acceleration and Velocity Functions

According to the Doyle log rule , the volume V in broad feet of a log of length L (feet) and diameter D (inches) at the small end is V= (D-4/4)^2 *L Find the rate at which the volume is changing with respect to D for a 12-foot long log whose smallest diameter is a.) 8 inches, b.) 16 inches, c.) 24 inches, and d.) 36 inche

### Linear Momentum of a Billiard Ball

A billiard ball approaches the rail at a speed of 15 m/s and an angle of 60 degrees, but rebounds at a speed of 10 m/s and an angle of 50 degrees. What is the change in momentum and use components?

### Basic Physics - Speed; Velocity; Distance

Attached: physics1: Calculating speed, velocity physics2: Calculating height, slope, distance physics3: 1 question using velocity/speed to calcuate for distance

### Paths Through a Uniform Magnetic Field, Solenoids and Net Magnetic Field

1) The figure (*see attachment) shows 11 paths through a region of uniform magnetic field. One path is a straight line; the rest are half circles. The table (*see attachment) gives the masses, charges and speeds of the 11 particles that take these paths through the field in the direction shown. Which path corresponds to which pa

### Rates of Change : Velocity and Displacement

1.) Suppose a car starts from a stop sign and moves along a straight road. Assume the distance traveled in t seconds is given by s (t) + t^2 = 3t. a.) How far has the car traveled after 5 seconds? [ find s(5) ] b.) The speed of the car at exactly 10 seconds after "flooring it", can be estimated by finding the average speed

### Dynamics (Angular Velocity, Angular Acceleration)

2 practice quiz problems which I need help on. Please give explanation of each problem as well as the answer: 1) Member AB rotates about pin A at a constant 10 rad/s. What is the acceleration of point C at the instant shown? a) 13.4m/s^2 b) 7.51m/s^2 c) 17.2 m/s^2 d) 11.5 m/s^2 e) 9.63 m/s^2 2) Wheel A rotates counte

### Dynamics Problems

Please see attached file for problems.

### Noether's theorem

Translate Noether's theorem into Hamiltonian mechanics. That is, define a symmetry for Hamiltonian mechanics (by translating the Lagrangian-definition), and prove that symmetries give rise to conserved observables.

### Kinematics Physics Experiments

Francesca, who likes physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from Dulles Airport . She notices that the string makes an angle of 25° with respect to the vertical while the aircraft accelerates for takeoff, which takes about 13.5 seconds. Estimate the takeoff spee

### Free Fall Speed Height

A student drops a ball from a height of 14.0m. How long does it take to hit the ground? What is its speed just as it hits the ground?

### Wave parameters and equation

1) A transverse traveling wave on a cord is represented by D = 0.48 sin (5.6x +84t) where D and x are in meters and t in seconds. For this wave determine (a) the wavelength (b) the frequency (c) velocity (magnitude and direction) (d) amplitude and (e) maximum and minimum speeds of particles of the cord.

### Projectile Motion - Magnitude and Angle

A light plane is headed due south with a speed relative to still air of 280 km/h. After 1 hour, the pilot notices that they have covered only 150 km and their direction is not south but southeast. What is the wind velocity? Find the magnitude (km/h) and angle (° north of east).

### A Swimmer's Projectile Motion

A swimmer is capable of swimming 0.95 m/s in still water. (a) If she aims her body directly across a 150 m wide river whose current is 0.55 m/s, how far downstream (from a point opposite her starting point) will she land? (m) (b) How long will it take her to reach the other side?(s)

### Projectile Motion - Velocity, Magnitude and Direction

A passenger on a boat moving at 1.20 m/s on a still lake walks up a flight of stairs at a speed of 0.50 m/s. The stairs are angled at 45° pointing in the direction of motion as shown. What is the velocity of the passenger relative to the water? Find the magnitude (m/s) and direction (above the water). See the attached for t

### Explanation of Projectile Motion

Question: A projectile is shot from the edge of a cliff 285 m above ground level, with an initial speed of vo=135 m/s and at an angle of 37.0 degrees with the horizontal, as shown in the attached figure. Please view attachment. a) Determine the time taken by the projectile to hit point P at ground level. b) Determine the ra

### Finding Velocity Vectors

An airplane is traveling 890 km/h in a direction 38.5 degrees west of north. (See the attachment for the figure). (a) Find the components of the velocity vector in the northerly and westerly directions. (b) How far north and how far west has the plane traveled after 5 h?

### A Ball is Thrown

(1) A ball is thrown horizontally from a height of 20.8m and hits the ground with a speed that is three times its initial speed. What was the initial speed? (2) A ball is shot from the ground into the air. At a height of 9.1m, the velocity is observed to be V = 7.9i + 5.1j in m/s (i horizontally, j upward). To what maximum he