Question

A 5.00 × 10⁵ , {kg} rocket is accelerating straight up. Its engines produce 1.25 × 10⁷ , {N} of thrust, and air resistance is 4.50 × 10⁶ , {N}. What is the rocket’s acceleration? Explicitly show how you follow the steps in the ProblemSolving Strategy for Newton’s laws of motion.

What is the rocket's acceleration?
a) 1.50 , {m/s}²
b) 2.50 , {m/s}²
c) 3.50 , {m/s}²
d) 4.50 , {m/s}²

Answer 1

The rocket's acceleration is calculated using Newton's second law of motion, with a net force of 8.00 × 106N resulting from the thrust minus air resistance, divided by the rocket's mass of 5.00 × 105 kg, yielding an acceleration of 16 m/s2.

Step-by-step explanation:

To solve for the rocket's acceleration, we apply Newton's second law of motion which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m*a). First, we calculate the net force on the rocket by subtracting the force due to air resistance from the thrust produced by the engines. The net force (Fnet) is calculated as follows:

Fnet = Thrust - Air Resistance

Fnet = 1.250 × 107 N - 4.50 × 106 N

Fnet = 8.00 × 106 N

Now, using Newton's second law, we find the acceleration (a) by dividing the net force by the mass (m) of the rocket:

a = Fnet / m

a = 8.00 × 106 N / 5.00 × 105 kg

a = 16 m/s2

Therefore, the acceleration of the rocket is 16 m/s2, which is not listed in the options provided. It appears there may have been an error in the options given, as they do not match the calculated result.