A 1.11.1​-kilogram mass has just been dropped from the roof of a building. I need to catch it after it has fallen exactly 9696 meters. If I weigh 8484 kilograms and start running at 99 meters per second as soon as the object is​ released, how far away can I stand and still catch the​ object?

(a) Calculate for a proton that has a momentum of (b) What is its speed? Such protons form a rare component of cosmic radiation with uncertain origins.

(a) Show that tidal force on a small object of mass m, defined as the difference in the gravitational force that would be exerted on m at a distance at the near and the far side of the object, due to the gravitational at a distance R from M, is given by Ftidal=2GMmR3r where r is the distance between the near and far side and rR .(b) Assume you are fallijng feet first into the black hole at the center of our galaxy. It has mass of 4 million solar masses. What would be the difference between the force at your head and your feet at the Schwarzschild radius (event horizon)? Assume your feet and head each have mass 5.0 kg and are 2.0 m apart. Would you survive passing through the event horizon?

A single-stage rocket of mass 308 metric tons (not including fuel) carries a payload of 3150 kg to low-Earth orbit. The exhaust speed of the rockets cryogenic propellant is 3.20 103 m/s. a. If the speed of the rocket as it enters orbit is 8.00 km/s, what is the mass of propellant used during the rockets burn? b. The rocket is redesigned to boost its exhaust speed by a factor of two. What is the mass of propellant used in the redesigned rocket to carry the same payload to low-Earth orbit? c. Because the exhaust speed of the redesigned rocket is increased by a factor of two, why is the fuel consumption of the redesigned rocket not exactly half that of the original rocket?