a stone is dropped from rest from the top of a tower 19.6m high.the distance travelled during the last second of its fall is.................

To find the distance traveled by a stone during the last second of its fall from a height of 19.6 meters, we can use the principles of physics related to free fall under gravity. Let’s break this down step-by-step to understand how to approach this problem effectively.

The Basics of Free Fall

When an object falls freely from a height, it accelerates due to the force of gravity, which is approximately 9.8 m/s². The stone is dropped from rest, meaning its initial velocity (u) is 0 m/s. The height of the tower (h) is given as 19.6 m.

Calculating the Total Time of Fall

First, we need to determine how long it takes for the stone to fall the entire distance of the tower. We can use the following equation of motion:

• h = ut + (1/2)gt²

Substituting the known values:

• h = 19.6 m
• u = 0 m/s
• g = 9.8 m/s²

Now, the equation simplifies to:

• 19.6 = 0 + (1/2)(9.8)t²

Solving for t²:

• 19.6 = 4.9t²
• t² = 19.6 / 4.9 = 4
• t = √4 = 2 seconds

Finding the Distance Traveled in the Last Second

Next, we want to find out how far the stone falls during the last second of its fall. To do this, we can calculate the distance fallen in the first 2 seconds and then subtract the distance fallen in the first second.

Distance Fallen in 2 Seconds

Using the earlier equation:

• h = ut + (1/2)gt²
• h = 0 + (1/2)(9.8)(2²) = (1/2)(9.8)(4) = 19.6 m

Distance Fallen in 1 Second

Now, calculate the distance for the first second:

• h = 0 + (1/2)(9.8)(1²) = (1/2)(9.8)(1) = 4.9 m

Calculating the Distance of the Last Second

To find the distance traveled during the last second, we subtract the distance fallen in the first second from the total distance:

• Distance in the last second = Total distance - Distance in the first second
• Distance in the last second = 19.6 m - 4.9 m = 14.7 m

So, the distance traveled during the last second of its fall is 14.7 meters.

Recap of Key Points

• The stone takes 2 seconds to fall from a height of 19.6 meters.
• The distance it falls in the last second of its fall is 14.7 meters.

By understanding these calculations, we see how the motion of falling objects can be analyzed using the equations of motion. If you have any more questions or if there's anything else you'd like to explore, feel free to ask!