A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) is m, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity ve (relative to the rocket). A model for the velocity of the rocket at time t is given by the equation v(t)=−gt−veln(m−rt/m) wher e g is the acceleration due to gravity and t is not too large. If g=9.8ms^2, m=30,000 kg, r=170kgs and ve=3,000ms. Required:
Find the height of the rocket one minute after liftoff. 

Samir watches a 100-minute movie on his spaceship. maria's spaceshipe flies in the same direction as samir's spaceship but she observes his move to last 125 minutes and his spaceship to be 40 m long. how long does samir observe his own spaceship to be? according to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does marias voyage take according to samir?

Hydrogen and helium are both members of?

To practice problem-solving strategy 10.1 for energy conservation problems. a sled is being held at rest on a slope that makes an angle θ with the horizontal. after the sled is released, it slides a distance d1 down the slope and then covers the distance d2 along the horizontal terrain before stopping. find the coefficient of kinetic friction μk between the sled and the ground, assuming that it is constant throughout the trip.