Rain is falling vertically down on a car moving at 11 m/s. Tracks made by the raindrops on the side window of the car are inclined at 55 degrees with the vertical. Find the speed of the raindrop relative to the ground.
Vr = (11m/s)/cos(90-55) = 13.4 m/s.
To find the speed of the raindrop relative to the ground, we can use the concept of vector addition.
Let's break down the motion of the raindrop and the car into two components: vertical and horizontal.
The vertical component of the raindrop's motion is simply due to gravity and can be calculated using the equation:
v_vertical = v * sin(θ)
where v is the velocity of the car (11 m/s) and θ is the angle the tracks are inclined at with the vertical (55 degrees).
Substituting the given values, we get:
v_vertical = 11 m/s * sin(55 degrees)
≈ 11 m/s * 0.819
≈ 9.01 m/s
The horizontal component of the raindrop's motion does not contribute to its speed relative to the ground since rain is falling vertically in this case.
Therefore, the speed of the raindrop relative to the ground is equal to its vertical component speed:
Speed of raindrop relative to the ground = v_vertical = 9.01 m/s