Final answer:
To calculate the magnitude of the vertical acceleration of the block of mass m1, you need to consider the mass of the block and the tension in the string. Use the equations of motion to find the acceleration of the system and then calculate the tension in the string.
Step-by-step explanation:
In order to calculate the magnitude of the vertical acceleration of the block of mass m1, we need to consider several factors, including the mass of the block and the tension in the string.
First, we'll use the equations of motion to find the acceleration of the system. The acceleration can be determined using the equation: a = (m2 - m1) * g / (m1 + m2), where g is the acceleration due to gravity.
Once we have the acceleration, we can calculate the tension in the string using the equation: T = m1 * a + m1 * g.