Billiard ball A of mass mA = 0.130 kg moving with speed vA = 2.80 m/s strikes ball B, initially at rest, of mass mB = 0.135 kg . As a result of the collision, ball A is deflected off at an angle of 27.5 ∘ with a speed vA1 = 2.15 m/s .

A)Taking the x axis to be the original direction of motion of ball A, write down the equation expressing the conservation of momentum for the components in the x direction. Assume the velocity of ball B after collision is vB1.

Express your answer symbolically in terms of the variables mA, mB, vA, vA1, vB1, θA, and θB.

B)Write down the equation expressing the conservation of momentum for the components in the y direction.

Express your answer symbolically in terms of the variables mA, mB, vA, vA1, vB1, θA, and θB.

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

Karen is running forward at a speed of 9 m/s. she tosses her sweaty headband backward at a speed of 20 m/s. the speed of the headband, to the nearest whole number relative to a stationary observer watching karen

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