Answer :
Answer:
a = 39.2 m/s²
Explanation:
The takeoff acceleration of a missile or a rocket can be expressed by the equation
- a = V₀/m * Δm/Δt - g
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
Final answer:
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 is 49 m/s².
Explanation:
To calculate the takeoff acceleration of an Antiballistic missile (ABM), we can use the equation for the thrust of a rocket, which equals the rate of expelled mass (Am/Δt) multiplied by the exhaust velocity (ve). The acceleration can then be calculated by dividing the thrust by the mass of the rocket (m). In this case, the thrust equals the rate of expelled mass (196 kg/s) times the exhaust velocity (2.50×10³ m/s), resulting in a thrust of 4.9×10⁵ Newtons. Therefore, the acceleration (a) of the ABM is the thrust (f) divided by the mass (m) of the ABM (10,000 kg). That is, a = f/m = 4.9×10⁵ N / 10,000 kg = 49 m/s².
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