Pallavi's Movements Analysis
Pallavi's journey involves several directional movements. To find the distance and direction of her college library from the candy shop, we need to calculate her net displacement.
Candy Shop Location Calculation
Let the college library be the origin (0, 0) on a coordinate plane, with North as the positive Y-axis and East as the positive X-axis.
- Initial movement: 70 m North. Pallavi is at (0, 70).
- Second movement: 60 m East. Pallavi is at (60, 70).
- Third movement: 45 m North. Pallavi is at (60, 70 + 45) = (60, 115).
- Fourth movement: 60 m West. Pallavi is at (60 - 60, 115) = (0, 115).
Pallavi stops at this point (0, 115) to buy candies. This is the location of the candy shop relative to the library. The subsequent 50 m North movement occurs after she leaves the candy shop and is not relevant for determining the library's position relative to the candy shop.
Library Position from Candy Shop
The candy shop is located at coordinates (0, 115) relative to the library at (0, 0).
The question asks for the distance and direction of the college library from the candy shop.
We need to find the displacement vector pointing from the candy shop's location to the library's location.
Displacement vector = (Library Coordinates - Candy Shop Coordinates)
Displacement vector = ($0 - 0$, $0 - 115$) = (0, -115)
Distance and Direction Result
The displacement vector (0, -115) means Pallavi needs to move 0 m horizontally (East/West) and 115 m vertically downwards (South) from the candy shop to reach the library.
The distance is the magnitude of this vector:
Distance = $\sqrt{(0)^2 + (-115)^2} = \sqrt{0 + 13225} = \sqrt{13225} = 115$ m.
The direction is indicated by the negative Y component, which corresponds to South.
Therefore, the college library is 115 m South from the candy shop.
Similar Questions
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Important Questions from Direction and Distance
What is the direction of U with respect to P?
What is the shortest distance between R and T?
If a person walks 3m towards the North from point V, takes a right turn and walks for another 15m, which of the following points would he reach?
In which direction is Amit facing at point F?
What is the distance between the starting point and the end point?
