You are riding in the back of an open pick-up truck in the snow as you pass your friend's house. Despite the fact that it is snowing you know that he has a habit of being in his bedroom with the light on and his bedroom window open. Being as you are riding in an open truck in the snow, and being the kind of friend you are, you decide to surprise him with a snowball. Naturally, you want this snowball to enter his room and fly straight across to the other side. You know that to do this you must release the snowball just as you pass his window. (You do have some smarts.) You also know that, to avoid drawing attention from the police since you are violating the law by riding in the back of an open truck the pickup is travelling at the legal limit of 40.0 Km/hr. You also have just come from a sports complex where you have tested your throwing ability to be 66.0 Km/hr. What is the direction in which you must throw the ball in order to accomplish your purpose? Express your answer in degrees. Take zero degrees to be straight towards the window, (i.e. perpendicular to the truck movement) with positive angles being toward the direction of the truck movement and negative angles away from the truck movement.

To determine the direction in which you must throw the snowball, we need to consider the relative velocities of the truck and the snowball.

Let's break down the velocities:

1. The velocity of the truck: 40.0 km/hr in the forward direction.

2. The velocity of the snowball (thrown by you): 66.0 km/hr.

To find the relative velocity of the snowball with respect to the truck, we subtract the velocity of the truck from the velocity of the snowball:

66.0 km/hr - 40.0 km/hr = 26.0 km/hr

Now, we need to analyze the components of this relative velocity to determine the angle at which you should throw the snowball.

Considering that the snowball needs to fly straight across to the other side of your friend's bedroom window, you want the horizontal component of the relative velocity to be zero. This means that the snowball should have no horizontal (sideways) movement relative to the truck.

Given that the truck is moving forward, if the snowball is to have no horizontal movement relative to the truck, it must be thrown in the same direction as the truck's forward motion. Therefore, the angle at which you should throw the snowball is 0 degrees (straight towards the window).

In summary, to accomplish your purpose, throw the snowball straight towards the window, parallel to the truck's movement, at an angle of 0 degrees.

To determine the direction in which you must throw the snowball, we need to consider the velocity of the snowball relative to your friend's house.

The velocity of the snowball relative to your friend's house can be found by subtracting the velocity of the truck from your throwing velocity:

Relative velocity = Throwing velocity - Truck velocity

Relative velocity = 66.0 km/hr - 40.0 km/hr
Relative velocity = 26.0 km/hr

Now, we need to break down this relative velocity into its horizontal and vertical components.

The horizontal component of the relative velocity will be the same as the velocity of the truck, which is 40.0 km/hr.

The vertical component of the relative velocity will be the difference between your throwing velocity and the velocity of the truck. Since the snowball must fly straight across to the other side, the vertical component of the relative velocity should be zero.

Let's denote the angle between the direction of the truck's movement and the direction in which you throw the ball as θ.

Using trigonometry, we can relate the vertical and horizontal components of the relative velocity to the throwing velocity:

Vertical component = Relative velocity * sin(θ)
Horizontal component = Relative velocity * cos(θ)

Since the vertical component should be zero, we can set up the following equation:

0 = Relative velocity * sin(θ)

Therefore, sin(θ) = 0, which means θ is either 0 or 180 degrees.

So, in order to accomplish your purpose of throwing the snowball into your friend's room and have it fly straight across to the other side, you should throw the ball either straight towards the window (0 degrees) or straight away from the window (180 degrees).