How Can the Windscreen Angle Prevent Rain from Entering the Cart?

[f(x)]

Homework Statement

A glass wind screen whose inclination with the vertical can be changed, is mounted on a cart as shown in figure. The cart moves uniformly along the horizontal part with a speed = 6 m/s. At what max. angle $$\ \theta$$ to the vertical can the wind screen be placed so that the rain drops falling vertically downwards with velocity = 2m/s DO NOT enter the cart ?
___________
|**********|\
|***CAR****|..\ <--WINDSCREEN
|**********|...\
|**********|
|___________|

2. What I need help with
This problem i am unable to start off
I am not able to judge the (relative) velocity vectors. I cannot decide the condition for the rain drops to not enter the car.
Thx for any help

 

[chaoseverlasting]

Assume that the car is at rest and the rain is falling at some angle to it. So, the vertical comp of the rain is given and the horizontal component will be that of the car (but with the direction reversed).

Now, assume that the rain falls in a straight line and that should give you something to work with.

 

[m2003]

I would approach this problem by first understanding the concept of relative velocity. Relative velocity is the velocity of an object with respect to another object or frame of reference. In this case, the rain drops are the object and the cart is the frame of reference.

To solve this problem, we need to consider the velocity of the rain drops relative to the cart. Since the cart is moving at a constant velocity of 6 m/s along the horizontal part, the rain drops will also have a horizontal velocity of 6 m/s relative to the cart. However, we also need to consider the vertical velocity of the rain drops.

The rain drops are falling vertically downwards with a velocity of 2 m/s. If we draw a vector diagram, we can see that the velocity of the rain drops relative to the cart would be the resultant of these two velocities. The magnitude of this resultant velocity can be found using the Pythagorean theorem, and we can use trigonometry to find the angle of this velocity relative to the cart.

Now, we need to determine the maximum angle at which the wind screen can be placed so that the rain drops do not enter the cart. This means that the relative velocity of the rain drops must be perpendicular to the wind screen. We can use the dot product of the relative velocity and the wind screen's normal vector to determine this condition.

Once we have the condition, we can use trigonometry to find the maximum angle at which the wind screen can be placed. This will be the angle at which the relative velocity of the rain drops is perpendicular to the wind screen and thus, the rain drops will not enter the cart.

In summary, to solve this problem, we need to understand the concept of relative velocity and use vector mathematics and trigonometry to determine the condition for the rain drops to not enter the cart. I hope this helps and good luck with your homework!