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dynamics Dynamics 1

The slotted arm OA rotates counterclockwise about O such that when theta=pi/4 arm OA is rotating with an angular velocity of theta dot and an angular acceleration of theta 2 dots. Determine the magnitude of the velocity of pin B at this instant. The motion of pin B is constrained such that it moves on the fixed circular surface and along the slot in OA. Determine the magnitude of the acceleration of pin B at this instant.

At the instant shown, cars A and B travel at speeds of 70 mi/h and 50 mi/h respectively. If B is increasing its speed by 1100 mi/h2, while A maintains a constant speed, determine the direction of the velocity and acceleration of B with respect to A. Car B moves along a curve having radius of curvature of .7 mi.

The 800 kg car at B is connected to the 350 kg car at A by spring coupling. Determine the stretch in the spring if the wheels of both cars are free to roll. Neglect the mass of the wheels. Determine the stretch in the spring if the brakes are applied to all four wheels of car B, causing the wheels to skid. Take (Uk)B=.4

If the 10-lb block slides down the plane with a constant velocity when theta=30 degrees, determine the acceleration of the block when theata equals 45 degrees.

Crossing a River. As shown, a swimmer wants to cross a river, from point A to point B. The distance d1 (between A and C) is 200 m, the distance d2 (between C and B) is 150 m, and the river's speed vr is 5.00 km/h. The swimmer's velocity relative to the water makes an angle of 45 degrees with respect to AC. To swim directly from A to B, what speed v2, relative to the river's speed, should the swimmer have?

Rocket Height. A rocket, initially at rest on the ground, accelerates straight upward with a constant acceleration of 34.3 m/s^2. The rocket accelerates for a period of 10.0 s before exhausting its fuel. The rocket continues its ascent until its motion is halted by gravity. The rocket then enters free fall. Find the maximum height, ymax, reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity of 9.810 m/s^2.

A particle is moving along a straight line such that its velocity is defined as v=(-4s^2) m/s, where s is in meters. If s=2m when t=0, determine the velocity as a function of time. Determine the acceleration as a function of time.

A bicycle travels along a straight road where its velocity is described by the v-s graph. Construct the a-s graph for the same time interval.

At the instant shown, cars A and B travel at speeds of 70 mi/h and 50 mi/h respectively. If B is increasing its speed by 1100 mi/h2, while A maintains a constant speed, determine the direction of the velocity and acceleration of B with respect to A. Car B moves along a curve having radius of curvature of .7 mi.

The 800 kg car at B is connected to the 350 kg car at A by spring coupling. Determine the stretch in the spring if the wheels of both cars are free to roll. Neglect the mass of the wheels. Determine the stretch in the spring if the brakes are applied to all four wheels of car B, causing the wheels to skid. Take (Uk)B=.4

If the 10-lb block slides down the plane with a constant velocity when theta=30 degrees, determine the acceleration of the block when theata equals 45 degrees.

Crossing a River. As shown, a swimmer wants to cross a river, from point A to point B. The distance d1 (between A and C) is 200 m, the distance d2 (between C and B) is 150 m, and the river's speed vr is 5.00 km/h. The swimmer's velocity relative to the water makes an angle of 45 degrees with respect to AC. To swim directly from A to B, what speed v2, relative to the river's speed, should the swimmer have?

Rocket Height. A rocket, initially at rest on the ground, accelerates straight upward with a constant acceleration of 34.3 m/s^2. The rocket accelerates for a period of 10.0 s before exhausting its fuel. The rocket continues its ascent until its motion is halted by gravity. The rocket then enters free fall. Find the maximum height, ymax, reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity of 9.810 m/s^2.

A particle is moving along a straight line such that its velocity is defined as v=(-4s^2) m/s, where s is in meters. If s=2m when t=0, determine the velocity as a function of time. Determine the acceleration as a function of time.

A bicycle travels along a straight road where its velocity is described by the v-s graph. Construct the a-s graph for the same time interval.

The position of a particle is defined by r={5cos(2t)i+4sin(2t)j} m, where t is in seconds and the arguments for the sine and cosine are given in radians. Determine the magnitudes of the velocity and acceleration of the particle when t=1s. Also, prove that the path of the particle is elliptical.

A particle moves along the curve y=x-x^2 /400, where x and y are in ft. If the velocity component in the x direction is vx=2ft/s and remains constant, determine the magnitudes of the velocity and acceleration when x=20 ft.

The baseball player A hits the baseball with va=40 ft/s and theata A=60 degrees. When the ball is directly above of player B he begins to run under it. Determine the constant speed vB and the distance d at which B must run in order to make the catch at the same elevation at which the ball was hit.

The boy at A attempts to throw a ball over the roof of a barn with an initial speed of vA=15 m/s. Determine the angle at which the ball must be thrown so that it reaches its maximum height at C. Also, find the distance d where the boy should stand to make the throw.

The train passes point B with a speed of v=20 m/s which is decreasing at at=-.5m/s^2. Determine the magnitude of acceleration of the train at this point.

A particle is traveling along a circular curve having a radius of 20m. If it has an initial speed of 20 m/s and then begins to decrease its speed at the rate of at=(-.025s)m/s^2, determine the magnitude of the acceleration of the particle 2s later.

The jet plane is traveling with a constant speed of 110 m/s along the curved path. Determine the magnitude of the acceleration of the plane at the instant it reaches point A (y=0).

A particle moves along a circular path of radus 5 ft. If its position is teata=e^.5t (rad), where t is in seconds, determine the magnitude of the particle's acceleration when theata = 90 degrees.

A particle moves along the curve y=x-x^2 /400, where x and y are in ft. If the velocity component in the x direction is vx=2ft/s and remains constant, determine the magnitudes of the velocity and acceleration when x=20 ft.

The baseball player A hits the baseball with va=40 ft/s and theata A=60 degrees. When the ball is directly above of player B he begins to run under it. Determine the constant speed vB and the distance d at which B must run in order to make the catch at the same elevation at which the ball was hit.

The boy at A attempts to throw a ball over the roof of a barn with an initial speed of vA=15 m/s. Determine the angle at which the ball must be thrown so that it reaches its maximum height at C. Also, find the distance d where the boy should stand to make the throw.

The train passes point B with a speed of v=20 m/s which is decreasing at at=-.5m/s^2. Determine the magnitude of acceleration of the train at this point.

A particle is traveling along a circular curve having a radius of 20m. If it has an initial speed of 20 m/s and then begins to decrease its speed at the rate of at=(-.025s)m/s^2, determine the magnitude of the acceleration of the particle 2s later.

The jet plane is traveling with a constant speed of 110 m/s along the curved path. Determine the magnitude of the acceleration of the plane at the instant it reaches point A (y=0).

A particle moves along a circular path of radus 5 ft. If its position is teata=e^.5t (rad), where t is in seconds, determine the magnitude of the particle's acceleration when theata = 90 degrees.

The car travels along the circular curve of radius r=400 ft with a constant speed of v=30 ft/s. Determine the angular rate of rotation of dot theata of the radial line r and the magnitude of the car's acceleration.

When theata=15 degrees, the car has a speed of 50 m/s which is increasing at 6 m/s^2. Determine the angular velocity of the camera tracking the car at this instant.

A ball is thrown vertically upward with a speed of 15 m/s. Determine the time of flight when it returns to its original position.

A particle moves along a straight line such that its acceleration is a=(4(t^2)-2) m/s, where t is in seconds. When t=0, the particle is located 2 m to the left of the origin, and when t=2s, it is 20 m to the left of the orgin. Determine the position of the particle when t=4s.

A ball is released from the bottom of an elevator which is traveling upward with a velocity of 6 ft/s. If the ball strikes the bottom of the bottom of the elevator shaft in 3 s, determine the height of the elevator from the bottom of the shaft at the instant the ball is released. Also, find the velocity of the ball when it strikes the bottom of the shaft.

If a particle has an initial velocity of 12 ft/s to the right at s0=0, determine its position when t=10s, if a=2 ft/s^2 to the left.

A particle starts from rest and travels along a straight line with an acceleration a=(30-.2v) ft/s^2, where v is in ft/s. Determine the time when the velocity of the particle is v=65 ft/s.

A sphere is fired downwards into a medium with an initial speed of 27 m/s. If it experiences a deceleration of a=-6t m/s^2, where t is in seconds, determine the distance traveled before it stops.

Ball A is thrown vertically upward from the top of a 30-m-high-building with an initial velocity of 5 m/s. At the same instant another ball B is thrown upward from the ground with an initial velocity of 20 m/s. Determine the height from the ground and the time at which they pass.

When theata=15 degrees, the car has a speed of 50 m/s which is increasing at 6 m/s^2. Determine the angular velocity of the camera tracking the car at this instant.

A ball is thrown vertically upward with a speed of 15 m/s. Determine the time of flight when it returns to its original position.

A particle moves along a straight line such that its acceleration is a=(4(t^2)-2) m/s, where t is in seconds. When t=0, the particle is located 2 m to the left of the origin, and when t=2s, it is 20 m to the left of the orgin. Determine the position of the particle when t=4s.

A ball is released from the bottom of an elevator which is traveling upward with a velocity of 6 ft/s. If the ball strikes the bottom of the bottom of the elevator shaft in 3 s, determine the height of the elevator from the bottom of the shaft at the instant the ball is released. Also, find the velocity of the ball when it strikes the bottom of the shaft.

If a particle has an initial velocity of 12 ft/s to the right at s0=0, determine its position when t=10s, if a=2 ft/s^2 to the left.

A particle starts from rest and travels along a straight line with an acceleration a=(30-.2v) ft/s^2, where v is in ft/s. Determine the time when the velocity of the particle is v=65 ft/s.

A sphere is fired downwards into a medium with an initial speed of 27 m/s. If it experiences a deceleration of a=-6t m/s^2, where t is in seconds, determine the distance traveled before it stops.

Ball A is thrown vertically upward from the top of a 30-m-high-building with an initial velocity of 5 m/s. At the same instant another ball B is thrown upward from the ground with an initial velocity of 20 m/s. Determine the height from the ground and the time at which they pass.

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