Classical Mechanics Answers

Answer in three decimal places

1.If block A has a velocity of 8.1 ft/sec to the right, determine the velocity of cylinder B. The velocity of B is positive if downward, negative if upward.

v_B = __ ft/sec

2.At a certain instant, the velocity of cylinder B is 0.91 m/s down and its acceleration is 3.69 m/s² up. Determine the corresponding velocity and acceleration of block A. The velocity and acceleration of A are positive if down the slope and negative if up the slope.

v_A= _ m/s

a_A= _ m/s²

Answers should be in three decimal numbers

1.The car A has a forward speed of 23 km/h and is accelerating at 2.7 m/s². Determine the velocity and acceleration of the car relative to observer B, who rides in a nonrotating chair on the Ferris wheel. The angular rate Ω = 3.8 rev/min of the Ferris wheel is constant.

v_A/B = (  _i +  _j) m/s

a_A/B = (  _i + _j) m/s²

2. Starting from the relative position shown, aircraft B is to rendezvous with the refueling tanker A. If B is to arrive in close proximity to A in a 3.0-minute time interval, what absolute velocity vector should B acquire and maintain? The velocity of tanker A is 257 mi/hr along the constant-altitude path shown.

y = 9350'

x = 2360'

v_B = (  _i +  _j) mi/hr

1.Car A rounds a curve of 129-m radius at a constant speed of 42 km/h. At the instant represented, car B is moving at 83 km/h but is slowing down at the rate of 4.9 m/s². Determine the velocity and acceleration of car A as observed from car B.

v_A/B =( _ i + _j) m/s

a_A/B =( _i + _j) m/s²

2.The jet transport B is flying north with a velocity v_B = 505 km/h when a smaller aircraft A passes underneath the transport headed in the 68^° direction shown. To passengers in B, however, A appears to be flying sideways and moving east. Determine the magnitudes of the actual velocity of A and the velocity which A appears to have relative to B.

Aircraft A is going in northeast direction

v_A = _ km/h

v_A/B =  _ km/h

Explain concisely, why a gun recoils after firing.

Two blocks of mass 0.30 kg and 0.20 kg are moving towards each other along a frictionless horizontal surface with velocities Of 0.50 m.s^-1 and 1.00 m.s^-1 respectively. Find the final velocity and direction of each block after collision if the collision is elastic. Create a simple diagram before and after the collision.

A 2-kg ball B traveling at 22m.s^-1 Overtakes a 4-kg ball traveling in the same direction at 10m.s^-1 Find the velocity of each ball after collision.

A bullet with a mass of 4 grams (g) is fired from a gun of mass 5kg with a velocity of 600m/s^-1 What is the velocity of recoil of the gun?

A force given as 2F - t - 4 = 0 acts horizontally on an object from (2,0) to (5,0). Find the impulse of the force

Find the law of motion of a particle in the field U(x)= – Bx 2 , if the full

energy equals to zero (B is positive constant).

4.     A coyote jumps over the edge of a cliff with a speed of 20 m/s. It hits the surface of the canyon 15 s later.

(a) Calculate the vertical speed of the coyote when it reaches the canyon surface.

(b) How high is the cliff?

(c) How far from the foot of the cliff will the coyote land?

5.     An aircraft flying horizontally at 150 m/s, drops a bomb which hits the target after 8 s.

Find:

a)   the distance travelled horizontally by the bomb

b)   the vertical speed of the bomb at impact

c)   the distance travelled horizontally by the aircraft as the bomb fell