A car travels due east with a speed of 42.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 70.0° with the vertical. Find the velocity of the rain with respect to the following reference frames. (Enter the magnitude of the velocity.)

Question

A car travels due east with a speed of 42.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 70.0° with the vertical. Find the velocity of the rain with respect to the following reference frames. (Enter the magnitude of the velocity.)

(a) the car

(b) the Earth

Answer 1

To find the velocity of the rain with respect to the car, we can break down the velocity into its horizontal and vertical components.

Given that the car is traveling due east, we can assume that the horizontal component of the velocity of the rain with respect to the car is the same as the velocity of the car itself, which is 42.0 km/h.

To find the vertical component of the velocity of the rain with respect to the car, we need to calculate the component of the rain's velocity that is perpendicular to the car's windows. We can do this using trigonometry.

Since the angle between the raindrops and the vertical is given as 70.0°, we can use the sine of the angle to find the vertical component of the rain's velocity. The sine of an angle is equal to the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the vertical component of the velocity is the opposite side.

Let's calculate it:

Vertical component = (Length of hypotenuse) * sin(70.0°)

Since we don't have the length of the hypotenuse, we can assume it to be the same as the speed of the raindrops, as the rain is falling vertically with respect to the Earth. Let's assume the speed of raindrops to be 'v'.

Vertical component = v * sin(70.0°)

Now, we can substitute the given information into the equation:

Vertical component = v * sin(70.0°)

To find the magnitude of the velocity of the rain with respect to the car, we can use the Pythagorean theorem:

Magnitude of velocity = √(Horizontal component squared + Vertical component squared)

Magnitude of velocity = √((42.0 km/h)² + (v * sin(70.0°))²)

Now, let's calculate the magnitude of the velocity of the rain with respect to the car.