From inside your apartment, you watch rain fall straight down at a constant speed of 9 m/s. Your friend L calls you as she is driving toawards the west at a constant of 90 km/hr. What with what velocity does L see the rain fall as she looks out her driver's side window?
I know I'm trying to find the velocity relative to L driving. I just don't know where to start. How would the velocity of the rain change?
Be sure to take care of units conversions.
From L's point of reference, the rain has the x component from her driving plus the y component of the rain falling. Find the resultant vector.
The velocity of the rain with respect to someone in the car is the vector sum of the downward rain velocity (9 m/s) and the car's speed, 90000m/3600 s = 25 m/s. Use the Pythagorean theorem for the resultant
To find the velocity of the rain as observed by your friend L, who is driving towards the west, we need to consider the concept of relative velocities.
Relative velocity refers to the motion of one object with respect to another object. In this case, we need to determine the relative velocity of the raindrop with respect to your friend L's car.
The rain is falling straight down with a velocity of 9 m/s. However, from L's perspective in her moving car, the raindrop appears to be moving both downward and horizontally due to her own motion.
To calculate the relative velocity, we need to break down the velocity into two components: one along the downward direction (vertical) and one along the horizontal direction (horizontal).
Let's assume that your apartment is to the north of L's location. Since L is driving towards the west, her horizontal velocity is in the westward direction and has a magnitude of 90 km/hr (which we will convert to m/s later). The vertical component of L's velocity remains zero as she is not moving up or down.
Now, we can calculate the relative velocity of the raindrop as observed by L using vector addition.
1. Convert L's horizontal velocity from km/hr to m/s:
Speed = 90 km/hr = (90 * 1000) / 3600 m/s = 25 m/s (rounded to two decimal places)
2. The raindrop's vertical velocity is unaffected by L's motion, so it remains 9 m/s.
3. Combine the horizontal and vertical components using the Pythagorean theorem:
Relative Velocity = √(Horizontal Velocity^2 + Vertical Velocity^2)
Relative Velocity = √(25^2 + 9^2) m/s
= √(625 + 81) m/s
= √(706) m/s
≈ 26.58 m/s (rounded to two decimal places)
Therefore, your friend L sees the rain fall with a velocity of approximately 26.58 m/s towards the driver's side window as she looks out while driving towards the west at a constant velocity of 90 km/hr.