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 2.50×103 m/s?

a = 39.2 m/s²

Explanation:

The takeoff acceleration of a missile or a rocket can be expressed by the equation

Where V₀ is the exhaust velocity, m is the mass of the missile, Δm is the mass of gas expelled during a timelapse Δt, and g is gravitational acceleration.

All required data is given by the problem, so now we solve for a:

a = 2.50x10³m/s ÷ 10,000kg * 196kg ÷ 1s - 9.8m/s²

a = 39.2 m/s²