At a certain instant of time the mass of a rocket going up vertically is 100 kg. If it is ejecting 5 kg of gas per second at a speed of 400 m/s, the acceleration of the rocket is  find the value of x ?

Let's solve the problem step by step:

Step 1: Given information

• Mass of the rocket (m) = 100 kg
• Rate of gas ejection (dm/dt) = 5 kg/s
• Ejection speed of gas (v) = 400 m/s

Step 2: Applying Newton's second law According to Newton's second law, the force acting on an object is equal to the product of its mass and acceleration. In this case, the force acting on the rocket is the force generated by the ejection of gas.

Force (F) = Rate of change of momentum (dp/dt)

Step 3: Calculating the rate of change of momentum The rate of change of momentum can be calculated by multiplying the rate of gas ejection with the ejection speed.

dp/dt = (dm/dt) * v

Substituting the given values: dp/dt = (5 kg/s) * (400 m/s)

Step 4: Calculating the acceleration The acceleration of the rocket can be calculated by dividing the rate of change of momentum by the mass of the rocket.

a = (dp/dt) / m

Substituting the given values: a = [(5 kg/s) * (400 m/s)] / 100 kg

Step 5: Simplifying the expression a = (2000 kg m/s) / 100 kg

Step 6: Calculating the value of x To find the value of x, we need to simplify the expression further.

a = 20 m/s

Therefore, the value of x is 20.