A rocket has a total mass of 1.01  105 kg and a burnout mass of 1.14  104 kg, including engines, shell and payload. The rocket blasts off from Earth and exhausts all its fuel in 4.31 min, burning the fuel at a steady rate with an exhaust velocity of ve= 4.66  103 m/s. (a) If air friction and gravity are neglected, what is the speed of the rocket at burnout? m/s(b) What thrust does the engine develop at liftoff? N(c) What is the initial acceleration of the rocket if gravity is not neglected? m/s2(d) Estimate the speed at burnout if gravity isn't neglected. m/s

A spaceship's orbital maneuver requires a speed increase of 1.05 ✕ 103 m/s. If its engine has an exhaust speed of 2.45 ✕ 103 m/s, determine the required ratio  Mi Mf  of its initial mass to its final mass. (The difference  Mi − Mf  equals the mass of the ejected fuel.)

A 66.0-kg athlete leaps straight up into the air from a trampoline with an initial speed of 7.5 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. (a) What are the interacting objects and how do they interact? This answer has not been graded yet. (b) Select the height at which the athlete's speed is 7.5 m/s as  y = 0.  What is her kinetic energy at this point? JWhat is the gravitational potential energy associated with the athlete? J(c) What is her kinetic energy at maximum height? JWhat is the gravitational potential energy associated with the athlete? J(d) Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer. m(e) Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer. m/s

A 130 lb person sitting in a 150 lb iceboat fires a gun, discharging a 2 oz bullet horizontally. If the bullet speed leaving the gun is 1200 ft/s, what will be the speed of the boat after the bullet is fired, if we assume no friction? The correct answer is 0.54 ft/s

The 0.5-kg ball is fired from the tube at A with a velocity of v = 6 m/s. If the coefficient of restitution between the ball and the surface is e = 0.8, determine the height h after it bounces off the surface. v = 6 m/s 2 m 130° B C h

A gun fires a 21-gram bullet on a 1.8 kg wooden block hanging vertically at the end of string (The other end of the string is attached to a ceiling). The bullet embeds in the block, which swings upward a height of H. The speed of the bullet when leaving the gun is 250 m/s. Find H.

A spaceship’s orbital maneuver requires a speed increase of 1.20 x 10^3 m/s. If its engine has an exhaust speed of 2.50 x 10^3 m/s, determine the required ratio Mi/Mf of its initial mass to its final mass. (The difference Mi - Mf equals the mass of the ejected fuel.)

A spaceship's orbital maneuver requires a speed increase of 1.30 ✕ 103 m/s. If its engine has an exhaust speed of 2.55 ✕ 103 m/s, determine the required ratio  Mi Mf  of its initial mass to its final mass. (The difference  Mi − Mf  equals the mass of the ejected fuel.)

If a rocket engine ejects gases at a rate of 29 kg/s, how fast must the gaseous exhaust be moving if the thrust produced is sufficient to allow a 2.7 x 105 kg rocket to rise slowly from the earth when aimed straight up? Express your answer in km/s.