A SpaceX rocket with an initial mass of m0 uses its engines to hover, stationary, just above the ground. (a) Write down a differential equation for the rocket’s mass using the condition that the thrust must balance the force of gravity. Assume the exhaust speed vex is a constant. (b) The rocket burns fuel and hovers until the final mass is mf . Solve for the amount of time it is able to hover. (c) Calculate the hover time for a rocket that burns an amount of fuel equal to 30% of its initial mass, with an exhaust speed of 2000 m/s.

A 0.726-kg rope 2.00 meters long lies on a floor. You grasp oneend of the rope and begin lifting it upward with a constant speedof 0.710 m>s. Find the position and velocity of the rope’s centerof mass from the time you begin lifting the rope to the time thelast piece of rope lifts off the floor. Plot your results. (Assume therope occupies negligible volume directly below the point where itis being lifted.)

There are no numerical values assigned to the variables in this problem. A block of mass m1 is projected with a velocity vi at the top of the wedge. When the block reaches the horizontal surface its velocity vf to the right while the wedge moves with a velocity v2 of to the left. (a). What is the velocity of the once it reaches the horizontal surface? Your answer must be in terms of relevant variables. (b). What is the height h the wedge in terms of the relevant variables?

Assume that the velocity V of fall of an object depends on the height H throughwhich it falls, the gravity g, and the mass m of the object. Find an expression for V.

A parachutist of mass 60 kg free-falls from an airplane atan altitude of 5000 meters. He is subjected to an air resistance force that is proportional to his speed . Assumethe constant of proportionality is 10 (kg/sec). Find andsolve the differential equation governing the altitude of theparachuter at time t seconds after the start of his free-fall.Assuming he does not deploy his parachute, find his limiting velocity and how much time will elapse before he hitsthe ground.

A 3.0-kg block (A) is attached to a 1.0-kg block (B) by a massless spring that is compressed and locked in place, as shown in the figure. The blocks slide without friction along the x-direction at an initial constant speed of v = 2.0 m/s. At Lee A A 000 B ell time to 0 s, the positions of blocks A and B are %3D 1.2 m, respectively, at which point a mechanism releases the spring, and the blocks begin to XA.i = 1.0 m and xB.i = XB.r oscillate as they slide. If 2.0 s later block B is located at xB.f = 7.5 m, what will be the position xA.f %3D of block A? XA,f

Two boxes of mass 30.0kg (on the left) and 10.0kg (on the right) are at rest side by side. You apply aforce of 310N on the leftmost box for 5.0s and they both slide across the floor. The larger boxexperiences a force of kinetic friction of 180N, and the boxes accelerate at a rate of 1.75 m/s2[R]. Calculate the force of friction on the rightmostbox.

Please show work thank you

A 3 kg block sits on a level table and a string runs over the edge of the table on a pulley to a mass of 10 kg. Find the velocity of the hanging mass after 5 seconds if it starts at rest and if the coefficient of friction is 0.7.

A rocket in space consumes fuel and oxidizer at the rate of 2.15 x 104 kg/s with an exhaust speed of 3.30 x 10 m/s. (a) Find the thrust (in N) produced by the rocket's engine. (b) Find the acceleration (in m/s2) of the rocket at liftoff from Earth's surface, if its initial mass was 3.00 x 10° kg. (Enter the magnitude.) m/s?