Study the information given below carefully and answer the questions that follow: Kartick starts moving in a car from point A. He moves 30 km to the south and then turns left from point B and moves 50 km till point C. He then turns right and moves 60 km and then turns left from point D and moves 50 km till point E. He then turns right from point E and moves 20 km and then turns right from point F. He moves 150 km and then turns right from point G and moves 80 km till point H and stopped.
In which direction is point C with respect to point G?
To accurately determine the direction of point C with respect to point G, we must carefully trace Kartick's entire car journey, segment by segment, and map out the coordinates of each significant point. For simplicity, let's assume Kartick starts at point A, which we can designate as the origin $\left(0,0\right)$ on a coordinate plane. In this system, positive X-axis represents East, negative X-axis represents West, positive Y-axis represents North, and negative Y-axis represents South.
Kartick's Journey: Step-by-Step Movement Analysis
Let's break down Kartick's travel path to understand the changes in his position:
- From A to B: Kartick drives 30 km towards the South. His X-coordinate remains unchanged, and his Y-coordinate decreases by 30.
- From B to C: From point B, he turns left. Since he was moving South, a left turn means he now moves East for 50 km. His Y-coordinate remains unchanged, and his X-coordinate increases by 50.
- From C to D: At point C, he turns right. As he was moving East, a right turn means he now moves South for 60 km. His X-coordinate remains unchanged, and his Y-coordinate decreases by 60.
- From D to E: From point D, he turns left. Since he was moving South, a left turn means he now moves East for 50 km. His Y-coordinate remains unchanged, and his X-coordinate increases by 50.
- From E to F: At point E, he turns right. As he was moving East, a right turn means he now moves South for 20 km. His X-coordinate remains unchanged, and his Y-coordinate decreases by 20.
- From F to G: From point F, he turns right. Since he was moving South, a right turn means he now moves West for 150 km. His Y-coordinate remains unchanged, and his X-coordinate decreases by 150.
- From G to H: Finally, at point G, he turns right. As he was moving West, a right turn means he now moves North for 80 km and then stops at point H. His X-coordinate remains unchanged, and his Y-coordinate increases by 80.
Positioning Points: Coordinate Mapping of Kartick's Path
Let's map out the coordinates of each important point based on Kartick's movements, assuming A is $\left(0,0\right)$:
| Point | Movement from Previous Point | Coordinates $\left(X, Y\right)$ |
|---|---|---|
| A | Starting Point | $\left(0, 0\right)$ |
| B | 30 km South from A | $\left(0, 0 - 30\right) = \left(0, -30\right)$ |
| C | 50 km East from B | $\left(0 + 50, -30\right) = \left(50, -30\right)$ |
| D | 60 km South from C | $\left(50, -30 - 60\right) = \left(50, -90\right)$ |
| E | 50 km East from D | $\left(50 + 50, -90\right) = \left(100, -90\right)$ |
| F | 20 km South from E | $\left(100, -90 - 20\right) = \left(100, -110\right)$ |
| G | 150 km West from F | $\left(100 - 150, -110\right) = \left(-50, -110\right)$ |
| H | 80 km North from G | $\left(-50, -110 + 80\right) = \left(-50, -30\right)$ |
Direction of Point C with Respect to Point G
We need to find the direction of Point C $\left(50, -30\right)$ when observed from Point G $\left(-50, -110\right)$. To determine this, we calculate the change in X and Y coordinates from G to C:
- Change in X-coordinate $\left(\Delta X\right)$: We subtract the X-coordinate of G from the X-coordinate of C.
$\Delta X = X_C - X_G = 50 - \left(-50\right) = 50 + 50 = 100$ - Change in Y-coordinate $\left(\Delta Y\right)$: We subtract the Y-coordinate of G from the Y-coordinate of C.
$\Delta Y = Y_C - Y_G = -30 - \left(-110\right) = -30 + 110 = 80$
Since the change in the X-coordinate $\left(\Delta X = 100\right)$ is positive, Point C is located to the East of Point G.
Since the change in the Y-coordinate $\left(\Delta Y = 80\right)$ is also positive, Point C is located to the North of Point G.
When a point is both to the North and to the East of a reference point, its direction is said to be North-east.
Final Direction Conclusion
Based on the detailed analysis of Kartick's journey and the calculation of coordinates, Point C is in the North-east direction with respect to Point G.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
