a 65 kg male skater pushes a 45 kg female skater causing her to accelerate at a rate of 2.0 ms ^2 at what rate will the male skater accelerate?
To find the rate at which the male skater will accelerate, we can use the principle of action and reaction, also known as Newton's third law of motion.
According to Newton's third law, for every action, there is an equal and opposite reaction. This means that when the male skater pushes the female skater, she exerts an equal force on him in the opposite direction.
First, let's determine the force exerted by the female skater. We can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration:
Force = mass × acceleration
Given that the mass of the female skater is 45 kg and her acceleration is 2.0 m/s^2, the force is calculated as:
Force = 45 kg × 2.0 m/s^2 = 90 N
Since the force exerted by the female skater on the male skater is equal in magnitude but opposite in direction, the male skater will experience a force of 90 N.
Now, to find the male skater's acceleration, we can use Newton's second law again. Rearranging the formula, we get:
Acceleration = Force / mass
Given that the mass of the male skater is 65 kg, we can substitute the values into the equation:
Acceleration = 90 N / 65 kg
Calculating this, we find:
Acceleration ≈ 1.38 m/s^2
Therefore, the male skater will accelerate at a rate of approximately 1.38 m/s^2.