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Problems on RECTILINEAR MOTION

1. The velocity of the particle is given by where v is in meters per

second and t is in seconds plot the velocity v and acceleration (a) versus time (t) for the first 6 seconds of motion, and evaluate the velocity when a is zero.

2. The velocity of a particle moving in a straight line is decreasing at the rate of per

meter of displacement at an instant when the velocity is determine the

acceleration a of the particle at this instant. 3. A particle travelling a straight line encounters a retarding force which courses its velocity

decreases according to where t is the time in seconds during which

the force acts. Determine the acceleration a of the particle when t = 10sec and find the corresponding distance S which the particle has moved during the 10- sec interval. Plot velocity v as a function of time t for the first 10 sec.

4. The car is traveling at a constant speed Vo = 100km/hr on the level portion of the road.

When 6 percent incline is encountered, the driver doesn’t change the

throttle setting and consequently the car decelerates at the constant rate .

Determine the speed of the car a. 10 seconds after passing point A and,b. When s = 100m.

5. In an archers test, the acceleration of the arrow decrease linearly

with distance s from its initial value of 4800m/ at A up on

release to zero at B after a travel of 600mm. calculate the maximum velocity v of the arrow

6. Compute the impact speed of a body released from rest at an altitude h= 800km (a) assume a constant gravitational

acceleration and (b) account for the variation of g worth altitude.

Neglect the effects of atmospheric drag.

A

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Problems on CURVILINEAR MOTION

1. With what minimum horizontal velocity u can a boy throw a rock at A and have it just clear the obstruction at B?

2. A projectile is fined from the vertical tube mounted on the vehicle which is traveling at the constant speed u= 30km/hr. the

projectile leaves the tube with a velocity relative to the tube if air

resistance is neglected, show that the projectile will load on the vehicle at the tube location and the distance S traveled by the vehicle during the flight of the projectile.

3. A projectile is launched from point A with initial condition shows in the fig. Determine the slant distance S which location the point B of impact. Calculate the time of flight.

4. The muzzle velocity of a long rage rifle at A is U=400m/sec determine the two angles of

elevation which will permit the

projectile to hit the mountain target B

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5. A projectile is fired with a velocity u at right angle

to the slope, which is inclined at an angle with

the horizontal. Derive an expression for the distance R to the point of impact.

Problems on NORMAL AND TANGENTIAL COORDINATES (n – t)

1. The speed of a car increases uniformly with time from 50km/hr at A to 100km/hr at B during 10 seconds. The radius of curvature of the bump at A is 40m. if the magnitude of the total acceleration of the car’s mass center is the same at B as at A , compute the radius of

curvature of the dip in the road at B. The mass center

of the car is 0.6m from the road.

2. A space craft S is orbiting Jupiter is a circular path 1000km above the surface with a constant speed. Using the gravitational low calculate the magnitude v of its orbital velocity with respect to Jupiter. The diameter of Jupiter is 142984km and its surface level gravitational acceleration is

24.85m/

3. The baseball player releases a ball with the initial conditions shown in the fig. Determine radius of curvature of the trajectory

a. Just after the release vo y=0.0

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b. At the apex. For each case compute the time rate of change of the speed.

4. A small particle P starts from point O with negligible speed and increases its speed to a

value where y is the vertical drop

from 0. When x = 15m, determine the n – component of acceleration of the particle.

5. A ball is thrown horizontally from the top of 50m diff at A with a speed of 15m/sec and lands at point C. because of a strong horizontal wind the ball has a constant acceleration i9n the negative x – direction determine the radius of

curvature of the path of the ball at B where its

trajectory makes an angle of 450 with the horizontal. Neglect any effect of air resistance in the vertical direction.

Problems on POLAR COORDINATES

1. Motion of the sliding block P in the rotating radial slot is controlled by the power screw as shown. For instant represented,

, and r= 300mm. also the screw

turns at constant speed giving for this instant,

determine the magnitudes of the velocity v and acceleration a of

v. sketch v and A if =

2. An internal mechanism is used to maintain a constant angular rate about the z axis of the space craft as the telescopic booms are extended at constant rate. The length L is varied fro, essentially zero to 3m. The maximum acceleration to which the sensitive experiment

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modules P may be subjected is 0.011 determine the maximum allowable boom

extension rate L.

3. At the bottom of a loop in the vertical plane at an altitude of 400m, the original

airplane P has a horizontal velocity of 600km/hr and no horizontal acceleration. The radius of curvature of the loop is 1200m. For the radial tracking at O, determine the

recorded values of for this instant.

4. The small block P starts from rest at time t=0 at point A and moves up the incline with

constant acceleration a. Determine as a function

of time.

5. An earth satellite travelling in the elliptical orbit shown has a velocity v=17970km/hr as it passes the end of the semi-minor axis at A. The acceleration of the satellite at A is a=ar=-1.556m/sec2 as calculated from the gravitational law. For position A calculate the

values of and .

Problems on RELATIVE MOTION (TRANSLATING AXES)

1. The passenger aircraft B is flying east with a velocity vB=800km/h, a military jet travelling south with a velocity vA=1200km/hr, passes under B at a slightly lower altitude. What velocity does A appear to have a passenger in

B, and what is the direction of that apparent

velocity?

2. A sail boat moving in the direction shown in tacking the windward against a north wind. The log registers a hull speed of 6.5 knots a ‘telltale’ (light string tied to the rigging)

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indicates that the direction of apparent wind is 350 from the center line of the boat. What is the true wind velocity vw?

3. The shuttle orbiter A is in a circular orbit of altitude 320km, while space craft B is in geosynchronous circular orbit of altitude 36000km. determine the acceleration of B relative to a non-rotating observer in the shuttle A. Use go=9.823m/s2 for the surface level gravitational acceleration and R=6371km for the radius of the earth.

4. The space craft s approached the planet mars along a trajectory b-b in the orbital plane of mars with an absolute velocity of 19km/s Mars has a velocity of 24.1km/s along its trajectory a-a. Determine the angle b between the line of sight S-M and the trajectory b-b when mars appear from the space craft to be approaching head on.

Problems on CONSTRAINED MOTION OF CONNECTED PSRTICLES

1. If block A has a velocity of 0.6m/sec to the right, determine the velocity of cylinder B

2. For the pulley system shown each of the he cables at A and B is given a velocity of 2m/sec in the direction of the arrow. Determine the upward velocity v of the load m.

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3. Determine on expression for the velocity vA of the cart A down the incline interims of the upward velocity vB of the cylinder B.

4. Collars A and B slide along the fixed right angled roads and are connected by a card of length L Determine the acceleration ax of collar B as a function of if collar A is given a constant upward velocity vA

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