Ant climb up 5 stairs, each of length 20 cm and height 20 cm . Find the distance covered and displacement covered by ant ?
Part 1: Distance
=> When we talk about distance, we consider the length of the total path travelled. This means, we add up every time the ant goes up 20cm, and crosses the length of 20cm.
Since the distance travelled per stair is 40cm (20cm + 20cm), and there are a total of 5 stairs, the total distance travelled is 200cm (40cm x 5).
Part 2: Displacement
=> When we talk about displacement, we only consider the direct distance (the shortest path) from the start position to the end position.
So, we need to find the distance of the one straight line from the bottom of the first step to the top of the fifth. Consider the following triangle representing one step:
/|
/ |
/ | 20cm
/___|
20cm
Using the pythagorean theorum, the length of the hypotenuse (the direct line from start to finish for one stair) is the root of 800 (20^2 + 20^2), which comes out to be 20√2
Since there are five stairs, the total displacement is given by multiplying this number by 5, which gives up 100√2 cm.
=> As you will observe, the displacement is less than the distance.
Thanks
To find the distance covered by the ant, we need to calculate the total length of the stairs.
Since each stair has a length of 20 cm and the ant climbed 5 stairs, the total distance covered by the ant is:
Distance = Length of one stair * Number of stairs
Distance = 20 cm * 5 stairs
Distance = 100 cm.
To find the displacement covered by the ant, we need to calculate the shortest distance between the starting point and the end point of the ant's climb.
Since each stair has a height of 20 cm and the ant climbed 5 stairs, the total displacement covered by the ant is:
Displacement = Height of one stair * Number of stairs
Displacement = 20 cm * 5 stairs
Displacement = 100 cm.
Therefore, the distance covered by the ant is 100 cm, and the displacement covered by the ant is also 100 cm.
To find the distance covered by the ant, we can calculate the total length of the path it takes to climb up the stairs.
The distance covered on each step can be calculated using Pythagoras' theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the length of each step is given as 20 cm, and the height is also given as 20 cm. So we can calculate the distance covered on each step as follows:
Distance on each step = √(length^2 + height^2) = √(20^2 + 20^2) = √(400 + 400) = √800
Since the ant climbs up five steps, the total distance covered can be calculated by multiplying the distance covered on each step by the number of steps:
Total distance covered = Distance on each step * Number of steps = √800 * 5
To find the displacement covered by the ant, we need to consider only the straight-line distance between the starting point and the ending point. In this case, as the ant climbs up the stairs and ends up on a higher level, the displacement would be equal to the vertical height of the entire stairway, which is 20 cm.
So, to summarize:
Distance covered by the ant = √800 * 5
Displacement covered by the ant = 20 cm