Arocket 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−velnm−rtm

where g is the acceleration due to gravity and t is not too large? if g=9.8m/s2, m=29,000kg, r=170kg/s, and ve=2,900m/s.

what would the height of the rocket be one minute after liftoff?

An open cart is moving along a straight frictionless horizontal track. when rain starts falling vertically into the cart, what happens to the speed of the cart?

Acar travels in reverse. it covers 150 meters in 12 seconds what is the velocity of the car what is the speed of the car

Asilver dollar is dropped from the top of a building that is 1324 feet tall. use the position function below for free-falling objects. s(t) = −16t2 + v0t + s0 (a) determine the position and velocity functions for the coin. s(t) = v(t) = (b) determine the average velocity on the interval [1, 2]. ft/s (c) find the instantaneous velocities when t = 1 second and t = 2 seconds. v(1) = ft/s v(2) = ft/s (d) find the time required for the coin to reach the ground level. (round your answer to three decimal places.) t = s (e) find the velocity of the coin at impact. (round your answer to three decimal places.) ft/s