An airplane flies horizontally with a constant speed of 172.0 m/s at an altitude of 1390 m. a package is dropped out of the airplane. ignore air resistance. the magnitude of the gravitational acceleration is 9.8 m/s2. choose the right as positive x-direction. choose upward as positive y-direction keep 2 decimal places in all answers
(a) what is the vertical component of the velocity (in m/s) just before the package hits the ground? pay attention to the direction (the sign).
(b) what is the magnitude of the velocity (in m/s) (including both the horizontal and vertical components) of the package just before it hits the ground?

Aparticle travels in a circular orbit of radius 21 m. its speed is changing at a rate of 23.1 m/s2 at an instant when its speed is 37.2 m/s. what is the magnitude of the acceleration (in m/s? ) of the particle?

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?

Velocity is a description of both speed and direction, therefore it - a vector - a force arrow - the same as acceleration - a magnitude