Question

A rocket on Earth experiences an upward applied force from its thrusters. As a result of this force, the rocket accelerates upward at 2 m/s². Assume that there are no other upward forces exerted on the rocket and that wind resistance is negligible. Which of the following combinations of the rocket's mass (m_Rocket) and force from its thrusters (F_Thrusters) would result in an upward acceleration of 2 m/s²? Select two answers.

a) m_Rocket = 1 kg, F_Thrusters = 12 N
b) m_Rocket = 3 kg, F_Thrusters = 36 N
c) m_Rocket = 2 kg, F_Thrusters = 10 N
d) m_Rocket = 4 kg, F_Thrusters = 20 N

Answer 1

The correct combinations that result in an upward acceleration of 2 m/s² are options a) (m_Rocket = 1 kg, F_Thrusters = 12 N) and d) (m_Rocket = 4 kg, F_Thrusters = 20 N), determined by applying Newton's second law and considering Earth's gravitational force.

Step-by-step explanation:

To solve for the combinations that result in an upward acceleration of 2 m/s², we will use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object (m) multiplied by its acceleration (a). Mathematically, this is represented as F = ma, where F is the force applied by the thrusters, m is the mass of the rocket, and a is the acceleration. We also need to consider Earth's gravitational force, which is the weight of the rocket (W = m × g), where g is the acceleration due to gravity (9.81 m/s²).

From the given options, the correct combinations should satisfy the equation F_Thrusters = m_Rocket × a + m_Rocket × g:

For option a), F_Thrusters = 12 N and m_Rocket = 1 kg: 12 N = 1 kg × (2 m/s² + 9.81 m/s²) = 1 kg × 11.81 m/s², which confirms 12 N is the correct force.

For option d), F_Thrusters = 20 N and m_Rocket = 4 kg: 20 N = 4 kg × (2 m/s² + 9.81 m/s²) = 4 kg × 11.81 m/s², which also confirms 20 N is the correct force.

Hence, the correct options that would result in the rocket achieving an acceleration of 2 m/s² are a) (m_Rocket = 1 kg, F_Thrusters = 12 N) and d) (m_Rocket = 4 kg, F_Thrusters = 20 N).