8.7 Introduction to Rocket Propulsion

Antiballistic missiles (ABMs) are designed to have very large accelerations so that they may intercept fast-moving incoming missiles in the short time available. What is the takeoff acceleration of a 10,000-kg ABM that expels 196 kg of gas per second at an exhaust velocity of $2 . \text{50} \times \text{10}^{3} \text{m}/\text{s}?$

Calculate the increase in velocity of a 4000-kg space probe that expels 3500 kg of its mass at an exhaust velocity of $2 . \text{00} \times \text{10}^{3} \text{m}/\text{s}$. You may assume the gravitational force is negligible at the probe’s location.

Derive the equation for the vertical acceleration of a rocket.

How much of a single-stage rocket that is 100,000 kg can be anything but fuel if the rocket is to have a final speed of $8 . \text{00} \text{km}/\text{s}$, given that it expels gases at an exhaust velocity of $2 . \text{20} \times \text{10}^{3} \text{m}/\text{s}?$

(a) A 5.00-kg squid initially at rest ejects 0.250-kg of fluid with a velocity of 10.0 m/s. What is the recoil velocity of the squid if the ejection is done in 0.100 s and there is a 5.00-N frictional force opposing the squid’s movement. (b) How much energy is lost to work done against friction?