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# Velocity

### 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

### 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

### Equal masses of inflammable and non-inflammable material.

A body consists of equal masses M of inflammable and non-inflammable material. The body descends freely under gravity from rest. The combustible part burns at a constant rate of kM per second where k is a constant. The burning material is ejected vertically upwards with constant speed u relative to the body, and air resistance m

### A woman is standing in the ocean, and she notices that after a wave crest passes, five more crests pass in a time of 50.0s. The distance between two successive crests is 32 m. Determine, if possible, the wave's (a) period, (b) frequency, (c) wavelength, (d) speed, and (e) amplitude. If it is not possible to determine any of these quantities, then so state.

A woman is standing in the ocean, and she notices that after a wave crest passes, five more crests pass in a time of 50.0s. The distance between two successive crests is 32 m. Determine, if possible, the wave's (a) period, (b) frequency, (c) wavelength, (d) speed, and (e) amplitude. If it is not possible to determine any of t

### A Juggler is Juggling a Rod One End of Which is Burning

A juggler is juggling a uniform rod one end of which is coated in tar and burning. He is holding the rod by the opposite end and throws it up so that, at the moment of release, it is horizontal, its Center of Mass is traveling vertically up at speed vo and it is rotating with angular velocity wo. To catch it, he wants to arrange

### Resultant velocity of a rower crossing a river's current

See attached file for full problem description. a. Rower A wishes to cross a river directly to the opposite bank (east) a distance of 30m. (i.e. at 90 to the shore). The current is flowing NS at 2.6 m/s and he can sustain a rowing speed of 3 m/s.

### Physics Questions

2. A car 3.5 m in length approaches an intersection that is 20 m wide. The light turns yellow when the car's speed is 20 m/s and the front of the car is 50 m from the beginning of the intersection. If the driver steps on the brake, the car slows at -3.8 m/s2. If he instead steps on the gas pedal, the car accelerates at 2.3 m/s2.

### Acceleration, Velocity, and Speed

See attached file for full problem description. Acceleration: 1. A car goes from rest to 60 ft/sec in 30 seconds, what was its average acceleration? 2. A rocket accelerates at a rate of 200 m/sec^2 from rest for 20 seconds. What is its final velocity? 3. If the total change in velocity of an object was 50 m/sec for 10 seco

### Motion - Velocity and Speed

1. Select the quantity that has changed--velocity or speed-- for a car that travels north at 88 km/h and then turns east while continuing to move at 88km/h. 2. Infer how distance and speed in the motions of clock parts are used to measure time. 3. How can you use a speedometer and a clock to tell how far you've traveled i

### Speed, Time and Distance

Direction---Velocity: List the given and unknown values, perform any necessary conversions, write the equation for speed, insert the known values into the equation, and solve. 1. Find the velocity in meters per second of a swimmer who swims exactly 110 m toward the shore in 72 s. 2. Find the velocity in meters per secon

### Algebra - calculating velocity

If a rock is thrown upward with an initial velocity of 32 feet per second from the top of a 40-foot building, write the height equation. The formula is s = -16t^2 + v o t + s o.

### Vertical Circular Motion

In an automatic clothes drier, a hollow cylinder moves the clothes on a vertical circle (radius r = 0.27 m), as the drawing shows. The appliance is designed so that the clothes tumble gently as they dry. This means that when a piece of clothing reaches an angle of above the horizontal, it loses contact with the wall of the cyli

### Angular Displacement of a Baseball

A pitcher throws a curveball that reaches the catcher in 0.53 s. The ball curves because it is spinning at an average angular velocity of 335 rev/min (assumed constant) on its way to the catcher's mitt. What is the angular displacement of the baseball (in radians) as it travels from the pitcher to the catcher?

### impulse applied to volleyball

A volleyball is spiked so that its incoming velocity of +3.8 m/s is changed to an outgoing velocity of -19 m/s. The mass of the volleyball is 0.38 kg. What impulse does the player apply to the ball?

### Physics: Velocity, Kinetic friction, Acceleration

1. Estimate the order of magnitude (exponential power) for the number of grains of salt in a salt shaker. 6. The world record for falling out of an airplane, without a parachute and surviving is 10,000m. If b is 0.13 N(s/m)^2, what is the terminal velocity of this person, assuming she has a mass of 70 kg? 9. consider pushi

### Frequency of Light

The red light associated with the Aurora Borealis is emitted by excited oxygen atoms at 6.60 X 10-7 m. What is the frequency of the light? Using scientific notation, (Round your answer to two decimal places) and write the exponent part as follows: x 10 to the _ power.

### Circular Motion

In uniform circular motion, the acceleration is perpendicular to the velocity at every instant. Is this true when the motion is not uniform, that is, when the speed is not constant?

### The Velocity of a Rocket at Parigee of an Elleptic Orbit

Problem # 4 - The rocket is traveling in a free-flight elliptical orbit about the earth such that e = 0.76 and Its perigee is 9Mm as shown. Determine its speed when it is at point B. Also determine the sudden decrease in speed the rocket must experience at A in order to travel in a Circular orbit about the earth.

### Angular velocity of a sphere and cylinder on an incline

A sphere and cylinder are released from rest on the ramp at t = 0. If each has a mass m and A radius r, determine their angular velocities at time t. Assume no slipping occurs. See attached file for full problem description.

### Rotational Motion of a Motor

Problem: The man stands on the platform at O and runs out toward the edge such that when he is at A, y = 5 ft, his mass center has a velocity of 2 ft/s and an acceleration of 3 ft/s^2, both measured with respect to the platform and directed along the y axis. If the platform has the angular motions shown, determine the velocity

### Two Particle System in Inertial Frames, and Newtonian Relativity

See the attached file. The question starts, Consider an isolated system comprising two particles of masses m1 and m2. Whose position vectors, in an inertial frame, are x1 and x2 and whose velocity vectors are v1 and v2. The interaction of the particles may be described by an energy function. E=1/2m1v1^2+1/2m2v2^2+U(x1,x

### Lorentz contraction for a length as measured by a fixed observer

A one-meter ruler moves at a speed c/2. In its own reference frame, it forms an angle of 45 degrees with its velocity. What is its length as measured by a fixed observer?

### Positve and Negative Acceleration and Velocity

1. Discuss the validity of each of the following statements. Provide examples to support the answers. a) If the acceleration of an object is positive, it is speeding up. If the acceleration of an object is negative, it is slowing down. b) If the velocity of an object is positive, it is moving away from the origin. If the vel

### S Inertial Frames

The following posting helps with problems involving inertial frames. See attached file for full problem description.

### Determining Time Given Velocity: Ball Example

When a ball is thrown vertically upward, its height (h, in feet) above the ground after t seconds is described by the mathematical formula h = - 16t2 + 96t + 80. At what times is the ball 103 feet above the ground?

### speed of boat in still water

Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4-mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water?

### relative velocity and work done by the train

A train moves along the tracks at a constant speed u. A woman on the train throws a ball of mass m straight ahead with a speed v with respect to herself. a) What is the kinetic energy gain of the ball as measured by a person on the train? b) By a person standing by the railroad track? c) How much work is done by the woman

### Magnitude of Average Velocity

A car moves from a point located 26.0 m from the origin and at an angle of 35.0 from the x-axis to a point located 56.0 m from the origin and at an angle of 60.0 from the x-axis in 2.50 s. What is the magnitude of the average velocity of the car? 12.7 m/s 13.7 m/s 16.1 m/s 18.3 m/s.

### Speed of Baseball Player

A baseball player is running to second base at 5.63 m/s. When he is 5.20 m from the plate he goes into a slide. The coefficient of kinetic friction between the player and the ground is 0.220. What is his speed when he reaches the plate? 4.47 m/s 3.04 m/s 1.96 m/s He stops before reaching the plate.