Answer :
Final answer:
The acceleration of an antiballistic missile at takeoff can be found using Newton's second law and conservation laws of momentum. The force the missile experiences due to the expelled gas can be calculated and substituted into the equation for force to solve for acceleration.
Explanation:
The takeoff acceleration of an antiballistic missile (ABM) can be determined by using Newton's second law, Force = mass x acceleration, or F = ma. We also know that momentum is conserved for the system. The change in momentum of the gas being expelled equals the change in momentum for the missile. Mathematically, that can be put as Force = rate of change of momentum which can also be written as F = Δp/Δt. The expelled gas creates a force as it leaves the missile, which in turn creates an upward force on the ABM give us: F = -dm/dt * V_exhaust. Substituting F = ma and rearranging for acceleration gives: a = -V_exhaust * dm/dt / m. If you plug in the values for m, dm/dt and V_exhaust, you'll be able to calculate the acceleration of the ABM in m/s².
Learn more about Physics of ABM acceleration here:
https://brainly.com/question/31963860
#SPJ11
