Question

# A man running on a horizontal road at 8 km/h finds the rain falling vertically. He increases his speed to 12 km/h and finds that the drops make an angle 30∘ with the vertical. Find the speed of the rain with respect to the road (in km/hr).

A
27
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
47
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
57
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
67
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C 4√7→Vrain, road=→Vrain, man+→Vman, road .....(i) The two situations given in the problem may be respresented by the following figure. →Vrain, road is same in magnitude and direction in both the figures. Taking horizontal components in equation (i) for figure (a). Vrain, roadsinα=8 km/h........(ii) Here α is angle of →Vrain, road with vertical. Now consider figure (b) OA⊥Vrain, man as shown. Taking components in equation (i) along the line OA. Vrain, roadsin(30∘+α)=12cos30∘ ....(iii) From (ii) and (iii), sin(30∘+α)sinα=12×√38×2 ⇒sin30∘cosα+cos30∘sinαsinα=3√34 ⇒12cotα+√32=3√34 i.e cot α=√32 or α=cot−1√32 From (ii), Vrain,road=8 km/hsinα =4√7 km/h

Suggest Corrections
1