Enter an expression for the initial acceleration of the rocket as it lifts vertically off of the ground with a mass m, assuming that it burns fuel at a rate R (kg/s) and shoots the resulting exhaust downward at speed vex.
When a rocket lifts off vertically, it experiences a force known as thrust, which is the result of the burning of fuel. The rocket expels the exhaust gases at high speed in one direction (downward), and by Newton's third law, the rocket experiences an equal and opposite force in the opposite direction (upward).
To calculate the initial acceleration of the rocket, we can use the rocket equation, which relates the thrust of the rocket to its mass and acceleration. Assuming that the rocket burns fuel at a rate R and shoots the resulting exhaust downward at speed Vex, the thrust can be expressed as:
T = R * Vex
At the start of the launch, the rocket is at rest, and the thrust is equal to the weight of the rocket and its fuel. Therefore, we have:
T = (m + Δm) * g
where m is the initial mass of the rocket, Δm is the mass of the fuel burned during a small time interval dt, and g is the acceleration due to gravity.
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