Two rockets with the same mass are. Accelerated. Rocket A accelerates twice as fast as Rocket B. Which statement is correct?
The motor in rocket A is four times as powerful as the motor and in rocket B
The motor in rocket A Is twice as powerful as the motor in rocket B
The motor in rocket A is half as powerful as the motor in rocket B
The motor in rocket A is half as Powerful as the motor in rocket B
Dude its The motor in rocket A is twice as powerful as the motor in rocket B.
in other words ANSWER B
The correct statement is: "The motor in rocket A is four times as powerful as the motor in rocket B."
To determine the correct statement, we can analyze the relationship between the acceleration of a rocket and the power of its motor.
Acceleration is directly proportional to the force applied to an object and inversely proportional to its mass. Mathematically, we can describe this relationship with the equation:
Acceleration = Force / Mass
In this scenario, both rockets have the same mass, so the equation becomes:
Acceleration = Force / Mass (constant)
Let's assume that Rocket B has an acceleration value of 'a'. Since Rocket A accelerates twice as fast, its acceleration value would be '2a'.
Now, let's analyze the relationship between acceleration and power. Power is defined as the rate at which work is done or energy is transferred. The formula for power is:
Power = Work / Time
Work is equal to the force applied multiplied by the distance covered. Since we are comparing the motors in Rocket A and Rocket B, we can consider that both rockets cover the same distance, and therefore the work done is the same. Thus, the equation becomes:
Power = (Force / Time)
Since both rockets have the same mass and Rocket A accelerates twice as fast as Rocket B, we can conclude that the force applied by Rocket A is two times greater than that applied by Rocket B. Therefore, the power formula becomes:
PowerA = (2 * ForceB) / Time
Now, let's compare the power of motor A and motor B:
To find the relationship between the power of the motors, we need to determine the ratio of PowerA to PowerB:
PowerA / PowerB = [(2 * ForceB) / Time] / [ForceB / Time]
Cancelling out the 'Time' term:
PowerA / PowerB = (2 * ForceB) / ForceB
The ForceB term cancels out, leaving:
PowerA / PowerB = 2
We conclude that the power of motor A is twice as powerful as the power of motor B. Therefore, the correct statement is:
The motor in rocket A is twice as powerful as the motor in rocket B.