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 D with respect to point H?
Kartick's Journey: Tracing the Path and Understanding Turns
To accurately determine the direction of point D with respect to point H, we must first trace Kartick's entire journey step-by-step. We will assign coordinates to each significant point, starting from point A, to visualize their exact positions on a two-dimensional plane. We assume positive X is East, negative X is West, positive Y is North, and negative Y is South.
Coordinate Plotting: Locating Each Point Accurately
Let's assume Kartick starts at Point A, which we place at the origin of our coordinate system (0,0). We then track his movements and turns to find the coordinates of each point (B, C, D, E, F, G, H).
| Segment | Movement Description | Direction | Distance | Start Point Coordinates | End Point Coordinates |
|---|---|---|---|---|---|
| 1 | Kartick starts from A, moves 30 km South | South ($\downarrow$) | 30 km | A (0,0) | B (0, -30) |
| 2 | From B, turns left, moves 50 km till C | East ($\rightarrow$) | 50 km | B (0, -30) | C (0 + 50, -30) = (50, -30) |
| 3 | From C, turns right, moves 60 km | South ($\downarrow$) | 60 km | C (50, -30) | D (50, -30 - 60) = (50, -90) |
| 4 | From D, turns left, moves 50 km till E | East ($\rightarrow$) | 50 km | D (50, -90) | E (50 + 50, -90) = (100, -90) |
| 5 | From E, turns right, moves 20 km till F | South ($\downarrow$) | 20 km | E (100, -90) | F (100, -90 - 20) = (100, -110) |
| 6 | From F, turns right, moves 150 km till G | West ($\leftarrow$) | 150 km | F (100, -110) | G (100 - 150, -110) = (-50, -110) |
| 7 | From G, turns right, moves 80 km till H | North ($\uparrow$) | 80 km | G (-50, -110) | H (-50, -110 + 80) = (-50, -30) |
Direction Calculation: Point D Relative to Point H
Now that we have the coordinates for all the points, we can determine the direction of point D with respect to point H. This means we imagine ourselves standing at point H and looking towards point D.
- Coordinates of Point D: $D = (50, -90)$
- Coordinates of Point H: $H = (-50, -30)$
To find the relative position of D from H, we subtract the coordinates of H from the coordinates of D:
Relative X-coordinate of D from H:
$\Delta X = X_D - X_H = 50 - (-50) = 50 + 50 = 100$
Relative Y-coordinate of D from H:
$\Delta Y = Y_D - Y_H = -90 - (-30) = -90 + 30 = -60$
So, the relative position of point D with respect to point H is $(100, -60)$.
- Since the $\Delta X$ (X-coordinate difference) is positive ($+100$), point D is to the East of point H.
- Since the $\Delta Y$ (Y-coordinate difference) is negative ($-60$), point D is to the South of point H.
Resulting Direction: Point D from Point H
When an object is to the East and South of a reference point, its direction is classified as South-east.
Therefore, point D is in the South-east direction with respect to point H.
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 :
