Given:
- The ball takes 0.2 seconds to cross the last 6 m before hitting the ground.
- Acceleration due to gravity (g) is 10 m/s^2.

To find:
The height from which the ball was dropped.

Solution:

Step 1: Understanding the problem
- The ball is dropped from a certain height and falls freely under the influence of gravity.
- The time taken to cross the last 6 m before hitting the ground is given as 0.2 seconds.

Step 2: Analyzing the motion of the ball
- The motion of the ball is governed by the equations of motion.
- The equation for the distance fallen by an object in free fall is given by:
- h = ut + (1/2)gt^2
- where h is the height, u is the initial velocity (which is 0 as the ball is dropped), g is the acceleration due to gravity, and t is the time taken.

Step 3: Applying the equation of motion
- In this case, the height h is the distance the ball fell before hitting the ground.
- The time taken t is given as 0.2 seconds.
- The acceleration due to gravity g is given as 10 m/s^2.

- Substituting the given values into the equation of motion, we have:
- h = 0 + (1/2)(10)(0.2)^2
- h = 0.01 m

Step 4: Converting the distance to height
- The distance fallen by the ball is given as 0.01 m.
- To find the height from which the ball was dropped, we subtract this distance from the total height.
- Since the total height is not given, we need to find it.

Step 5: Finding the total height
- The ball takes 0.2 seconds to cross the last 6 m before hitting the ground.
- Using the equation of motion, we have:
- 6 = 0 + (1/2)(10)(0.2)^2
- 6 = 0.02 m

Step 6: Calculating the height from which the ball is dropped
- The total height is given as 0.02 m.
- To find the height from which the ball was dropped, we subtract the distance fallen (0.01 m) from the total height:
- Height = Total height - Distance fallen
- Height = 0.02 - 0.01
- Height = 0.01 m

Step 7: Converting the height to meters
- The height is given in meters.
- Converting the height from meters to centimeters, we have:
- Height = 0.01 m * 100 cm/m
- Height = 1 cm

Step 8: Converting the height to kilometers
- The height is given in centimeters.
- Converting the height from centimeters to kilometers, we have:
- Height = 1 cm * (1 km/100000 cm)
- Height = 0.00001 km

Step 9: