(COLLAB) A new design of Saturn 13 rocket with mass 1.04 x10° kg has a propulsion engine that can eject gases at a constant speed of 230.15 m/s (vGas) by burning fuel at a rate of 4.19 x105 kg/s (dmdT). In full tank, the rocket can carry a fuel of mass 46.07 x10 ° kg. If this design exceeds the velocity of 11,200 m/s it can can successfully escape Earth's gravity. Determine if this is so. Find its maximum velocity (velyZ). (Pitch Angle = 0)

Find the escape speed of a projectile from the surface of Mars.

Find the escape speed of a projectile from the surface of Jupiter.

A suspicious physics student watches a stunt performed at an ice show. In the stunt, a performer shoots an arrow into a bale of hay (Fig. P11.24). Another performer rides on the bale of hay like a cowboy. After the arrow enters the bale, the balearrow system slides roughly 5 m along the ice. Estimate the initial speed of the arrow. Is there a trick to this stunt? FIGURE P11.24

Professional Application Ion-propulsion rockets have been proposed for use in space. They employ atomic ionization techniques and nuclear energy sources to produce extremely high exhaust velocities, perhaps as great as 8.00106 m/s. These techniques allow a much more favorable payload-to-fuel ratio. To illustrate this fact: (a) Calculate the increase in velocity of a 20,000-kg space probe that expels only 40.0-kg of its mass at the given exhaust velocity. (b) These engines are usually designed to produce a very small thrust for a very long time—the type of engine that might be useful on a trip to the outer planets, for example. Calculate the acceleration of such an engine if it expels 4.50106 kg/s at the given velocity, assuming the acceleration due to gravity is negligible.

A system consists of five particles. How many terms appear in the expression for the total gravitational potential energy of the system? (a) 4 (b) 5 (c) 10 (d) 20 (e) 25

A light balloon is filled with 400 m3 of helium at atmospheric pressure. (a) At 0C, the balloon can lift a payload of what mass? (b) What If? In Table 15.1, observe that the density of hydrogen is nearly half the density of helium. What load can the balloon lift if filled with hydrogen?

(a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y?

A person of mass m stands on a rope ladder that is hanging from a freely floating balloon of mass M. The balloon is initially at rest with respect to the ground. (The buoyant force on the personballoon system is countering the force of gravity.) a. In what direction will the balloon move if the person starts to climb the rope ladder at constant velocity v relative to the ladder? b. At what speed will the balloon move if the person starts to climb the rope ladder at constant velocity v relative to the ladder?

As it plows a parking lot, a snowplow pushes an ever-growing pile of snow in front of it. Suppose a car moving through the air is similarly modeled as a cylinder of area A pushing a growing disk of air in front of it. The originally stationary air is set into motion at the constant speed v of the cylinder as shown in Figure P8.32. In a time interval t, a new disk of air of mass m must be moved a distance v t and hence must be given a kinetic energy 12(m)v2. Using this model, show that the cars power loss owing to air resistance is 12Av3 and that the resistive force acting on the car is 12Av2, where is the density of air. Compare this result with the empirical expression 12DAv2 for the resistive force. Figure P8.32