A person standing on a road has to hold his umbrellat at ` 45^@` with the vertical to deep the rain away . He throws the umbtella and starts running at ` 30 ms^(-1)` . He find that the rain drops are hitting his head vertically. Fing the speed of the rain drops with respect to (a) road (b) the moving person.

Explanation

When person is at rest with respect to gorund, the rain is coming to him at an angle ` 45^@` with the vertcal. i.e. Along (OB) . When a person a fter throwing his umbrella runs on ground at ` 30 ms^(-1)`, the relatve velcity of rain w.r.t. person , ` v_(rp)` is along (OC) as shown in Fig. 2 ( c) . 92. ltbRgt Here` /_BOC = 45^@`
.
velocity of rain w.r.t. ground, ` vec_r = vec (OB)`
volcity of person w.r.t. ground, ` vec v_P = vec (OB)` ltbRgt where ` v_P = (OA) = 30 ms^(-1) = CB`
velocity of fain w.r.t. person, ` vec v_(rP) = vec (OP)`
In ` Delta OCB`, /_COB= 45^@ = /_OBC, so ` OC=CB`.
:. ` v_(rP) = OC = 30 ms^(-1)`
In ` Delta OCB`,
` OB= sqrt (OC^2 +CB^2) = sqrt (OC^@+OC^2)` ltbRgt ` = OC sqrt 2 = 30 sqrt 3 ms^(-1)`
:. ` v_r = 30 sqrt 2 ms^(-1)`.