Problem:
An object is dropped from a height h = 2R above the surface of the earth. Find the speed with which it will collide with the ground, neglecting the effect of air.

Solution:
To find the speed with which the object will collide with the ground, we need to consider the gravitational force acting on the object. Neglecting the effect of air, the only force acting on the object is the gravitational force.

Key Formula:
The formula to calculate the speed of an object in free fall is given by:

v = √(2gh)

Where,
v = speed of the object
g = acceleration due to gravity
h = height from which the object is dropped

Step 1: Identify the Given Parameters:
In this problem, we are given that the height from which the object is dropped is h = 2R.

Step 2: Calculate the Acceleration due to Gravity:
The acceleration due to gravity on the surface of the earth is approximately 9.8 m/s².

Step 3: Substitute the Values:
Substituting the given values into the formula, we have:

v = √(2 * 9.8 * 2R)

Simplifying,

v = √(39.2R)

Step 4: Final Answer:
Therefore, the speed with which the object will collide with the ground is √(39.2R).

Conclusion:
By neglecting the effect of air, we can calculate the speed with which an object will collide with the ground using the formula v = √(2gh), where g is the acceleration due to gravity and h is the height from which the object is dropped. In this problem, the height is given as 2R, and after substituting the values, we find that the speed is √(39.2R).