Fter its second booster has been fired, a space vehicle finds itself outside the earth’s atmosphere, moving
vertically upward at a speed v0 against gravity g. its total mass at that point is m0. at t = 0, the vehicle’s
third stage is turned on and the rocket burns propellant at a mass rate mrkg/s, ejecting gas from the exit
plane (area ae) at speed ve relative to the rocket.
show that if the gravitational acceleration remains essentially constant at the vehicle during the rocket firing,
the velocity v (t) of the vehicle after time t will be given by
m0 g[m0 − m(t)] v (t) − v0 = ve ln − m(t) m˙ r
where m(t) is the mass of the system at time t. assume that although the pressure of the gas at the rocket
exit plane is pe (the rocket exhaust is supersonic, and hence the pressure at the exit is not balanced with
the zero pressure of space), the effect of the finite exit plane pressure on the thrust is negligible.

American eels (anguilla rostrata) are freshwater fish with long, slender bodies that we can treat as uniform cylinders 1.0 m long and 10 cm in diameter. an eel compensates for its small jaw and teeth by holding onto prey with its mouth and then rapidly spinning its body around its long axis to tear off a piece of flesh. eels have been recorded to spin at up to 14 revolutions per second when feeding in this way. although this feeding method is costly in terms of energy, it allows the eel to feed on larger prey than it otherwise could. 1.a field researcher uses the slow-motion feature on her phones camera to shoot a video of an eel spinning at its maximum rate. the camera records at 120 frames per second. through what angle does the eel rotate from one frame to the next? 2. the eel is observed to spin at 14 spins per second clockwise, and 10 seconds later it is observed to spin at 8 spins per second counterclockwise. what is the magnitude of the eels average angular acceleration during this time? 3. the eel has a certain amount of rotational kinetic energy when spinning at 14 spins per second. if it swam in a straight line instead, about how fast would the eel have to swim to have the same amount of kinetic energy as when it is spinning? 4.a new species of eel is found to have the same mass but one-quarter the length and twice the diameter of the american eel. how does its moment of inertia for spinning around its long axis compare to that of the american eel?

Which configuration would produce an electric current? a) rotate a coil of copper wire between two magnets. b) connect a wire between a copper and zinc strip sitting in a beaker of water. c) connect a wire to the (+) positive end of a battery and the other end to a light bulb. d) connect a wire to the negative end of a battery and the other end to a light bulb.

Ascientific blank must be testable and capable of being proven false?