PROBLEM 8. The total weight of space shuttle including its payload mass and the empty external tank, and its empty two solid rocket boosters is mo = 428,100 lb. It is known that the external tank and the two solid rocket boosters initially holds m,(0) = 3,728,875 lb of fuel (that is the total weight of solid fuel plus liquid oxygen and hydrogen). The shuttle consumes its liquid and solid fuels at a constant rate of A, = 14,300 lb/s. Also, it is known that the shuttle thrust force is F, = 400,000 lb. (a) Use the Newton's 2nd law below to find the second order differential equation that describes the vertical position y of the space shuttle as a function of time. The shuttle is launched vertically upward from the ground as shown below, with the positive direction upward and the air resistance is ignored. The Earth's gravitational acceleration on its surface is g = 32.2 ft/s² and its radius is R = 4000 miles. Frotat (t) = [m(t). v] Fehrust Where, - Frotat(t) is the net force acting on the space shuttle that is the difference between thrust force F, and gravitational force Fg. - m(t) denotes the total mass of the rocket at time t given by m(t) = m, + m;(t) - m, is the constant mass of the shuttle including the mass of payload, the empty external fuel tank and rocket boosters. - m, (t) is the variable amount of liquid and solid fuels given by m, (t) = -Ast + m, (0) Fgravity F9 center of Earth

100% High pressure water and compressed air are delivered to some operating rooms. Bored one day, with no patients around, you take the cap off the nozzle to see what would happen. Water flows through the vertical pipe and nozzle and then exhausts into the air as shown in the diagram. The water pressure in the pipe at position 1 is 3 atm. The pressure when the water discharges to the air is 1 atm. Position 2 identifies the nozzle, 0.75 m above position 1, where the water flow has been constricted from an 8-cm diameter pipe to a 3-cm diameter nozzle. Assume that the free jet remains a stream of water with a 3-cm diameter. Assume no friction losses. Free jet -3 cm diameter 0.75 m a) Determine the mass flow rate of water through pipe at position 1 in kg/s. 3 atm 8 cm diameter b) Determine the height, h, the water jet can rise. c) Calculate the friction factor inside the 8-cm pipe and determine if the assumptions of negligible friction losses was reasonable. Water AR d 128 PM 10/3/2021…

(a) An automobile having a mass of 900 kg initially moves along a level highway at 100 km/h relative to the highway. It then climbs a hill whose crest is 50 m above the level highway and parks at a rest area located there. For the automobile, determine its changes in kinetic and potential energy, each in kJ. For each quantity, kinetic energy and potential energy, specify your choice of datum and reference value at that datum. Let g = 9.81 m/s².

A 0.4 kgkg piece of ice at -15 ∘C∘C is dropped from a height hh. Upon impact, 7.0 %% of its kinetic energy is converted into heat energy.     Part A If the impact transforms all of the ice into water that has a final temperature of 0 ∘C∘C, find hh. Express your answer in meters.