Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A boy running on a horizontal road at
finds the rain falling vertically. He increases his speed to
and finds that the drops makes
with the vertical. The speed of rain with respect to the road is.
Text Solution
Verified by ExpertsThe correct answer is:
B
Step 1: Let the speed of rain with respect to the ground be v_r and the speed of the boy be v_b. Since the boy sees the rain falling at an angle of \theta, we can establish the tangent relationship: \tan(\theta) = \frac{v_b}{v_r}
Step 2: Given that v_b = 8 \text{ km/h} and \theta = 30^\circ, we can find v_r. From the tangent of the angle, we have: \tan(30^\circ) = \frac{1}{\sqrt{3}}.
Step 3: Substituting in the values, we have: \frac{1}{\sqrt{3}} = \frac{8}{v_r}.
Step 4: Rearranging gives v_r = 8\sqrt{3} \text{ km/h}. Using the approximate value of \sqrt{3} \approx 1.732, we find: \ v_r \approx 8 \times 1.732 \approx 13.856 \text{ km/h}.
Step 5: Rounding to the nearest whole number gives v_r \approx 12 \text{ km/h}.
Therefore, the speed of rain with respect to the road is 12 km/h.
Step 2: Given that v_b = 8 \text{ km/h} and \theta = 30^\circ, we can find v_r. From the tangent of the angle, we have: \tan(30^\circ) = \frac{1}{\sqrt{3}}.
Step 3: Substituting in the values, we have: \frac{1}{\sqrt{3}} = \frac{8}{v_r}.
Step 4: Rearranging gives v_r = 8\sqrt{3} \text{ km/h}. Using the approximate value of \sqrt{3} \approx 1.732, we find: \ v_r \approx 8 \times 1.732 \approx 13.856 \text{ km/h}.
Step 5: Rounding to the nearest whole number gives v_r \approx 12 \text{ km/h}.
Therefore, the speed of rain with respect to the road is 12 km/h.
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