At the Earth's surface a 800 kg projectile is launched straight up at a speed of 9.00 km/s. Ignore air resistance and the rotation of the Earth a. What is the projectile's total mechanical energy at Earth's surface? J b. What is the projectile's maximum height (measured from the Earth's surface)? km c. How much work was done by the gravitational field as the projectile moved from the surface to its maximum height? J d. True/False: The projectile's maximum height depends on the projectile's mass? True

Awind turbine is initially spinning at a constant angular speed. as the wind's strength gradually increases, the turbine experiences a constant angular acceleration 0.173 rad/s2. after making 2870 revolutions, its angular speed is 132 rad/s. (a) what is the initial angular velocity of the turbine? (b) how much time elapses while the turbine is speeding up?

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?

Initially, a particle is moving at 5.33 m/s at an angle of 37.9° above the horizontal. two seconds later, its velocity is 6.11 m/s at an angle of 54.2° below the horizontal. what was the particle's average acceleration during these 2.00 seconds in the x-direction (enter first) and the y-direction?