a mass of gas emitted from the rear of toy rocket is initially 0.2kg/s. if the speed of the gas relative to the rocket is 40m/s and the mass of the rocket is 4 kg what is the initial acceleration of the rocket
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To find the initial acceleration of the rocket, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
In this case, the force acting on the rocket is the force exerted by the gas being emitted from the rear of the rocket. This force can be determined using the principle of conservation of momentum.
The mass of the gas emitted per second is given as 0.2 kg/s, and the speed of the gas relative to the rocket is given as 40 m/s. So, the rate at which momentum is being transferred to the rocket by the gas is (0.2 kg/s) x (40 m/s) = 8 kg·m/s.
According to Newton's third law of motion, this change in momentum of the gas is equal and opposite to the change in momentum of the rocket. Therefore, the force acting on the rocket due to the gas is 8 kg·m/s.
Since the mass of the rocket is 4 kg, we can now calculate the acceleration using Newton's second law: F = ma. Rearranging the equation, we have a = F/m.
Substituting the values, we have:
a = (8 kg·m/s) / 4 kg
a = 2 m/s²
So, the initial acceleration of the rocket is 2 m/s².
The reaction force is
F = Vexhaust*(mass flow rate)
= 40*0.2 = 8 Newtons
The acceleration rate is F/m = 2 m/s^2
Since that is less than g (which is 9.8 m/s^2), it won't leave the ground. It better have wheels if it is going anywhere.