Question

Unreasonable Results (a) What is the initial acceleration of a rocket that has a mass of 1.50×106kg at takeoff, the engines of which produce a thrust of 2.00×106N? Do not neglect gravity. (b) What is unreasonable about the result? (This result has been unintentionally achieved by several real rockets.) (c) Which premise is unreasonable, or which premises are inconsistent? (You may find it useful to compare this problem to the rocket problem earlier in this section.)(a) Rocket Acceleration: What is the initial acceleration of a rocket with a mass of 1.50×10⁶ kg at takeoff, given that its engines produce a thrust of 2.00×10⁶ N? (Do not neglect gravity.)

a) 0.33 m/s²
b) 1.33 m/s²
c) 2.00 m/s²
d) 3.33 m/s²

Answer 1

The initial acceleration of the rocket is 1.33 m/s², which is greater than Earth's gravitational acceleration. This is not possible in reality, as the rocket's engines cannot produce a thrust greater than the force of gravity on the rocket.

Step-by-step explanation:

The initial acceleration of a rocket can be found using Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration, F = ma. In this case, the thrust produced by the engines of the rocket is the net force acting on the rocket, so we can write the equation as:

F = ma

2.00 x 10^6 N = (1.50 x 10^6 kg)a

Simplifying, we find that the initial acceleration of the rocket is 1.33 m/s².

(b) The unreasonable aspect of this result is that the acceleration of the rocket is greater than the value of Earth's gravitational acceleration (9.8 m/s²), which means that the rocket's engines are able to produce a force greater than the force of gravity on the rocket. This is not possible in reality.

(c) The premise that is unreasonable is that the rocket's engines can produce a thrust greater than the force of gravity on the rocket, leading to an acceleration greater than Earth's gravitational acceleration.