A car travels due east with a speed of 35.0 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.
There are no following reference frames.
Pleas provide complete questions and show your work
the reference frames are 1) the car,
2) the earth.
I've got 3.54 m/s for part (1). but it is not correct. Thanks a million
To find the velocity of the rain with respect to the given reference frames, we need to decompose the velocity into its horizontal and vertical components.
Reference frame 1: Earth's frame of reference
In this reference frame, the velocity of the raindrops would be their actual velocity, which is vertical. Let's call it Vrain (vertical component of raindrop's velocity). The horizontal component of the raindrop's velocity in this frame would be 0, as raindrops are falling vertically. Therefore, the velocity of rain with respect to Earth's frame of reference is Vrain vertically and 0 horizontally.
Reference frame 2: Car's frame of reference
In this reference frame, we need to consider the velocity of the car and its effect on the raindrop's velocity. The car is moving due east with a velocity of 35.0 km/h. Let's call this velocity Vcar.
To determine the velocity of the raindrops with respect to the car's frame of reference, we need to subtract the horizontal component of the car's velocity from the horizontal component of the raindrop's velocity. Since the traces of the rain on the side windows make an angle of 70.0° with the vertical, the vertical and horizontal components of the raindrop's velocity can be determined using trigonometry.
The vertical component of the raindrop's velocity, Vrain_vertical, can be calculated using the equation: Vrain_vertical = Vrain * sin(70.0°)
The horizontal component of the raindrop's velocity, Vrain_horizontal, can be calculated using the equation: Vrain_horizontal = Vrain * cos(70.0°)
Now, the velocity of the raindrops with respect to the car's frame of reference can be obtained by subtracting the horizontal component of the car's velocity from the horizontal component of the raindrop's velocity.
Velocity of rain with respect to car's frame of reference = Vrain_horizontal - Vcar horizontally and Vrain_vertical vertically.
Note: The values of Vrain, Vcar, Vrain_horizontal, and Vrain_vertical should be converted to the same unit (e.g., km/h) before performing the calculations.