Question

Find the mean value of the velocity of a body falling freely from the altitude \(\mathrm{h}\) with the initial velocity \(\mathrm{v}_{0}\)

Short answer

Answer: The three steps to find the mean velocity of a freely falling body are: 1. Find the time of fall from the given height (h). 2. Determine the final velocity (v_final) after falling for the calculated time. 3. Calculate the mean velocity using the formula: v_mean = (v_initial + v_final) / 2.

Step-by-step solution

Find the time of fall

Use the position equation to determine the time required for the body to fall freely: \(\Delta x = v_0t + \frac{1}{2}at^2\) Substituting the values: \(h = v_0t + \frac{1}{2}gt^2\) Now, we need to solve for 't'.

Determine the final velocity

After getting the time 't', we will determine the final velocity (v_final) using the velocity-time formula: \(v_{final} = v_0 + at\) Here, we have 'g' as the acceleration which is due to gravity.

Calculate the mean velocity

Now, we can calculate the mean velocity (v_mean) using the formula: \(\mathrm{v}_{mean}=\frac{\mathrm{v}_{initial}+\mathrm{v}_{final}}{2}\) Substitute the values of the initial and final velocities and calculate the mean velocity. Following these three steps, you will be able to find the mean velocity of a body falling freely from an altitude (h) with an initial velocity (v_0).