Import Question JSON

Current Question (ID: 9673)

Question:

$\text{A man is walking on the road with a speed 3 m/s. Rain is falling vertically at speed 3 m/s. At what angle from the vertical, man has to hold his umbrella to avoid the rain drops?}$

Options:

1. $45°$
2. $30°$
3. $60°$
4. $90°$

Solution:

\text{Hint: Find the direction of rain w.r.t man} \text{Step 1: Assume direction for rain \& man} \text{Let x-axis be horizontal (direction of man's motion) and y-axis be vertical (downward direction of rain)} \vec{v}_r = +3\hat{j} \text{ m/s (rain velocity - vertically downward)} \vec{v}_m = 3\hat{i} \text{ m/s (man's velocity - horizontally)} \text{Step 2: Use relative velocity formula} \vec{v}_{r,m} = \vec{v}_r - \vec{v}_m = 3\hat{j} - 3\hat{i} \text{Step 3: Find the direction of } \vec{v}_{r,m} \text{The relative velocity vector has components: horizontal = -3, vertical = 3} \text{The angle } \theta \text{ from the vertical is given by:} \tan\theta = \frac{\text{horizontal component}}{\text{vertical component}} = \frac{3}{3} = 1 \theta = 45^{\circ} \text{Therefore, the man must hold his umbrella at } 45^{\circ} \text{ from the vertical to avoid rain drops.}

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}