Question

A man is traveling at 10.8km/hr in a topless car on a rainy day.He holds an umbrella at an angle of 37°to the vertical to protect himself from the rain which is falling vertically downwards. What is the velocity of the rain?Given:cos37°=4/5

Answer 1

Answer attached below.
Hope this helps.

Answer 2

Answer:

The velocity of the rain is $8.1km/hr$.

Explanation:

Given: Speed of the car = $v_c = 10.8km/hr$

speed f the rain = $v_R$

Angle from the vertical  $= 37^o$

$cos(37^o)=4/5$

$\implies sin(37^o)=3/5$

As,  $tan(\theta)=\frac{sin(\theta)}{\cos(\theta)}$

$\implies tan(37^o)=\frac{sin(37^o)}{\cos(37^o)}=\frac{\frac{3}{5} }{\frac{4}{5} }=\frac{3}{4}$

Now, the ratio of the vector $v_R$ and  $v_c$ is :      $\frac{v_c}{v_R} = tan(37^o)$

$\implies \frac{v_c}{v_R} = \frac{3}{4}$

$\implies v_R = \frac{3}{4}v_c$

$\implies v_R = \frac{3}{4}*10.8$

$\implies v_R =8.1km/hr$

The velocity of the rain is $8.1km/hr$.

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