A rectangular track is 40m long 30m broad.A man starts walking from one corner to another . Find the distance travelled and displacement.
corner to corner is one length and one breadth
... distance = 40 + 30
the diagonal is the hypotenuse of a 3-4-5 triangle
... displacement = √(30^2 + 40^2)
To find the distance traveled and displacement, we need to determine the path the man takes and the straight-line distance between the starting and ending points.
Step 1: Determine the path:
The man starts walking from one corner to another, so he walks along the length of the track (40m) and then along the width of the track (30m). This creates a right-angled triangle.
Step 2: Calculate the distance traveled:
To find the distance traveled, we need to calculate the length of the hypotenuse of the right-angled triangle, using the Pythagorean theorem: a^2 + b^2 = c^2.
In this case, one side (a) is 30m and the other side (b) is 40m.
c^2 = 30^2 + 40^2
c^2 = 900 + 1600
c^2 = 2500
c = √2500
c = 50
Therefore, the distance traveled by the man is 50m.
Step 3: Calculate the displacement:
Displacement is the straight-line distance between the starting and ending points.
In this case, the displacement is equal to the length of the hypotenuse, which we have already calculated to be 50m.
Therefore, the displacement of the man is 50m.
To find the distance travelled, we need to calculate the perimeter of the rectangular track which is the total length of all its sides.
The length of the track is given as 40 meters and the breadth is given as 30 meters.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, since opposite sides of a rectangle are equal, we can calculate the perimeter by adding the lengths of only two sides and then multiplying by 2.
Perimeter = 2 × (Length + Breadth)
Perimeter = 2 × (40 + 30) = 2 × 70 = 140 meters
Therefore, the distance travelled by the man is 140 meters.
Now let's calculate the displacement. Displacement is defined as the shortest distance between the initial and final positions, along with the direction.
In this case, the man starts walking from one corner to another, which means the initial and final positions are the diagonally opposite corners of the rectangle.
The diagonal of a rectangle can be calculated using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In the rectangle, the length and breadth form the two sides of the right-angled triangle, and the diagonal is the hypotenuse.
Using the Pythagorean theorem:
Diagonal^2 = Length^2 + Breadth^2
Diagonal^2 = 40^2 + 30^2
Diagonal^2 = 1600 + 900
Diagonal^2 = 2500
Taking the square root of both sides:
Diagonal = √2500 = 50 meters
Therefore, the displacement of the man is 50 meters.
To summarize:
Distance travelled = 140 meters
Displacement = 50 meters
𝗗𝗶𝘀𝘁𝗮𝗻𝗰𝗲 =𝟰𝟬𝗺+𝟯𝟬𝗺=𝟳𝟬𝘮
𝘋𝘪𝘴𝘱𝘭𝘢𝘤𝘦𝘮𝘦𝘯𝘵 𝘪𝘴 𝘵𝘩𝘦 𝘴𝘩𝘰𝘳𝘵𝘦𝘴𝘵 𝘥𝘪𝘴𝘵𝘢𝘯𝘤𝘦 𝘤𝘰𝘷𝘦𝘳𝘦𝘥 𝘣𝘦𝘵𝘸𝘦𝘦𝘯 𝘪𝘯𝘪𝘵𝘪𝘢𝘭 𝘢𝘯𝘥 𝘧𝘪𝘯𝘢𝘭 𝘱𝘰𝘴𝘪𝘵𝘪𝘰𝘯.
𝗗𝗶𝘀𝗽𝗹𝗮𝗰𝗲𝗺𝗲𝗻𝘁=√𝟰𝟬𝗺^𝟮+𝟯𝟬𝗺𝗺^𝟮
=𝟭𝟲𝟬𝟬𝗺+𝟵𝟬𝟬𝗺=√𝟮𝟱𝟬𝟬𝗺=𝟮𝟱𝗺