A bus with a vertical windshiled moves along in a rainstorm at speed V relative to the ground.
The raindrops fall vertically with a terminal speed of V' relative to the ground. At what angle do
the raindrops strike the windshield?
Well, let's think about this for a moment. If the bus is moving forward and the raindrops are falling vertically, they would appear to be coming in at an angle relative to the windshield. Let's call that angle "theta", because it's always more fun to throw some Greek letters into the mix.
Now, imagine you're sitting on the bus and looking out through the windshield. As the bus moves forward, the raindrops will be coming towards you at a certain speed. But since the bus is also moving, their speed relative to you (or the windshield, in this case) will be slightly lower.
So, if we break it down, we have two vectors here: the velocity of the raindrops relative to the ground (V') and the velocity of the bus relative to the ground (V). The angle at which the raindrops strike the windshield will be the angle between these two vectors.
Now, without getting too technical, we can determine this angle using trigonometry. The angle theta can be found using the arctangent function:
theta = arctan(V / V')
But wait, I almost forgot the most important part! Let's not take this too seriously, because we're talking about raindrops hitting a windshield here. It's like a mini water show happening in your view. So, maybe the real question is, at what angle does the bus driver start wishing they had brought an umbrella? 😄
To determine the angle at which the raindrops strike the windshield, we need to consider the motion of the bus and the raindrops relative to each other.
Here's how we can approach it:
1. Let's figure out the velocity of the raindrops relative to the bus. Since the raindrops fall vertically with a terminal speed of V' relative to the ground, and the bus is moving at speed V relative to the ground, the velocity of the raindrops relative to the bus is V' - V. This is because the raindrops' vertical velocity cancels out with the bus's vertical velocity.
2. The raindrops are falling vertically while the bus is moving horizontally. To find the angle at which the raindrops strike the windshield, we can compare the vertical and horizontal components of the raindrops' velocity relative to the bus.
3. The vertical component of the raindrops' velocity relative to the bus is V' - V (as mentioned earlier). The horizontal component remains unaffected by the bus's motion and is still zero.
4. We can use trigonometry to find the angle θ at which the raindrops strike the windshield. The vertical component is the opposite side (V' - V) and the horizontal component is the adjacent side (0). The angle θ is given by the ratio of opposite over adjacent, which is tan(θ) = (V' - V) / 0.
5. Since the horizontal component is zero, tan(θ) is undefined. This means that the raindrops will strike the windshield at a vertical angle (90 degrees) relative to the windshield.
So, in summary, the raindrops will strike the windshield at a vertical angle (90 degrees) relative to the windshield because the horizontal component of their velocity relative to the bus is zero.