# Find the magnitude of the velocity of the rain with respect to the car.A car travels due east with a horizontal speed of 57.1 km/h. Rain is falling vertically with respect to Earth. The traces of...

Find the magnitude of the velocity of the rain with respect to the car.

A car travels due east with a horizontal speed of 57.1 km/h. Rain is falling vertically with respect to Earth. The traces of the rain on the side windows of the car make an angle of 68.6 degrees with the vertical.

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### 2 Answers

A car travels due east with a horizontal speed of 57.1 km/h. Rain is falling vertically downwards with respect to Earth. Let the magnitude of velocity of the car be V. The traces of the rain on the side windows of the car make an angle of 68.6 degrees with the vertical.

The traces of rain that are formed on the side windows of the car making an angle of 68.6 degrees with the vertical are due to the combined effect of the horizontal velocity of the car as well as the vertical velocity of the rain.

tan 68.6 = 57.1/V

=> V = 57.1/tan 68.6

=> V = 22.37 km/h

The velocity of the rain is 22.37 km/h in a direction vertically downwards.

Speed of car = 57.1 Km/h

The angle at which rain makes on the side window = 68.6 dgrees with the vertical

Let the magnitude of velocity of rain relative to be "R" and "x" be the speed of car and "a" the angle of rain with vertical

Then x = Rcos(a)

=> 57.1 = R*cos(68.6)

=> R = 57.1/cos(68.6) Km/h = 156.5 Km/h

**Magnitude of velocity of rain relative to car = 156.6 Km/h**