Kirtaan walks from his house with a velocity of 2 m/s East for 30 seconds and then walks with a velocity of 8 m/s South for 10 seconds. At the end of these 40 seconds, how far from his house is Kirtaan?
Question
Kirtaan walks from his house with a velocity of 2 m/s East for 30 seconds and then walks with a velocity of 8 m/s South for 10 seconds. At the end of these 40 seconds, how far from his house is Kirtaan?
Solution
To solve this problem, we need to calculate the distance Kirtaan traveled in each direction and then use the Pythagorean theorem to find the total distance from his house.
Step 1: Calculate the distance Kirtaan traveled East. Distance = Speed * Time = 2 m/s * 30 s = 60 m
Step 2: Calculate the distance Kirtaan traveled South. Distance = Speed * Time = 8 m/s * 10 s = 80 m
Step 3: Use the Pythagorean theorem to find the total distance from his house. The Pythagorean theorem is a² + b² = c², where c is the hypotenuse of a right triangle, and a and b are the other two sides. In this case, the distance East is one side of the triangle, the distance South is the other side, and the total distance from his house is the hypotenuse.
So, c² = a² + b² = (60 m)² + (80 m)² = 3600 m² + 6400 m² = 10000 m²
Therefore, c = √10000 m² = 100 m
So, Kirtaan is 100 meters away from his house at the end of the 40 seconds.
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