A girl inside a room is looking at the window and sees a volleyball passing outside

the window of width w and height d. The ball appears from the upper left corner A of
the window and disappears at the lower right corner B in t0 second. The girl knows
that the ball has been kicked by a friend from a balcony at a height h above the upper
edge of the window. The ball was kicked t seconds before it appeared at A. Find t
under the hypothesis that viscosity is negligible.

DATA: h =5[m]; w=2[m];d=1.5[m]; t0 =1[s]

To find the value of t, we can use the concept of projectile motion. Since we are assuming negligible viscosity, we can neglect the effects of air resistance and treat the motion as a projectile.

First, let's break down the problem and understand the motion of the ball:

1. The ball is kicked from a height h above the upper edge of the window.
2. It takes t0 seconds for the ball to travel from the upper left corner A to the lower right corner B of the window.
3. The window has a width w and height d.

To find the time t it took for the ball to appear at point A after it was kicked, we need to consider the horizontal and vertical components of its motion separately.

Horizontal Motion:
In the x-direction (horizontal), the ball travels the width of the window w in time t0. Therefore, we can use the equation:

Distance = Speed * Time

Since the distance is w and the time is t0, we can write:

w = Speed * t0

Vertical Motion:
In the y-direction (vertical), we need to consider the height h and the time t.

The ball is kicked at time t before it appears at point A. Therefore, the total time it took for the ball to reach point A is t + t0.

Using the equation of motion:

Distance = Initial Velocity * Time + (0.5 * Acceleration * Time^2),

we can find the vertical distance traveled by the ball. The vertical distance is equal to the height h:

h = (0.5 * g * t^2),

where g is the acceleration due to gravity.

Now, we have two equations:

w = Speed * t0
h = (0.5 * g * t^2).

We can solve these equations simultaneously to find the value of t.

Here are the steps to find the value of t:

1. Substitute the known values:
- h = 5 m
- w = 2 m
- t0 = 1 s
- g ≈ 9.8 m/s^2 (acceleration due to gravity)

2. Solve the equation w = Speed * t0 for Speed:
Speed = w / t0

3. Substitute the value of Speed into the equation h = (0.5 * g * t^2):
5 = (0.5 * 9.8 * t^2)

4. Simplify the equation and solve for t:
5 = 4.9 * t^2
t^2 = 5 / 4.9
t = sqrt(5 / 4.9)

5. Calculate the numerical value of t using a calculator:
t ≈ 1.004 s (rounded to three decimal places)

Therefore, under the given hypothesis of negligible viscosity, it took approximately 1.004 seconds for the ball to be kicked before it appeared at point A.