A window is 50 long. A stone is falling from a height of 40 cm above the window.find the time taken by the stone to cross the window.

To find the time taken by the stone to cross the window, we can use the equations of motion.

Let's assume the initial velocity of the stone is 0 m/s (since it's falling) and the acceleration due to gravity is -9.8 m/s^2 (taking downward direction as negative).

We know the distance traveled is equal to the length of the window, which is 50 m. Additionally, since the stone falls from a height of 40 cm above the window, we can calculate the total distance traveled by the stone as:

Total distance = Distance above the window + Window length
= 40 cm + 50 cm
= 90 cm

However, we need to convert it to meters to maintain consistency with the other units, so the total distance is 0.9 m.

Now, we can use the equation of motion to find the time taken by the stone to cross the window:

Distance = Initial velocity * Time + (1/2) * Acceleration * Time^2

Since the initial velocity is 0 m/s, the equation simplifies to:

Distance = (1/2) * Acceleration * Time^2

Plugging in the values, we have:

0.9 m = (1/2) * (-9.8 m/s^2) * Time^2

Simplifying the equation further:

0.9 m = -4.9 m/s^2 * Time^2

Dividing both sides by -4.9 m/s^2:

Time^2 = -0.9 m / -4.9 m/s^2
Time^2 = 0.1837 s^2

Taking the square root of both sides to find the time:

Time = √(0.1837 s^2)
Time ≈ 0.428 s

Therefore, the time taken by the stone to cross the window is approximately 0.428 seconds.

To find the time taken by the stone to cross the window, we need to consider the vertical motion of the stone and use the equations of motion.

First, let's assume the positive direction to be upwards and the origin to be at the top of the window. Since the stone is falling downwards, its initial velocity (u) is 0 m/s, and the distance it needs to cross is the height of the window (h) minus the initial displacement (0.40 m).

Using the equation of motion for vertical motion, which is given by:

s = ut + (1/2)gt^2

Where:
- s is the displacement (h - 0.40)
- u is the initial velocity (0)
- t is the time taken
- g is the acceleration due to gravity (approximately 9.8 m/s^2)

Plugging in the values, we get:

(h - 0.40) = 0 + (1/2)(9.8)t^2
h - 0.40 = 4.9t^2

Now, let's rearrange the equation to solve for time:

t^2 = (h - 0.40) / 4.9
t = √[(h - 0.40) / 4.9]

Given that the height of the window is 50 cm (or 0.50 m), we can substitute this value into the equation:

t = √[(0.50 - 0.40) / 4.9]
t = √(0.10 / 4.9)
t = √0.0204
t ≈ 0.143 seconds

Therefore, the time taken by the stone to cross the window is approximately 0.143 seconds.

3upon7

d = (1/2) g t^2

how long to fall 90 cm = .9 m
.9 = (1/2)(9.81) t^2

how long to fall 40 cm = .4 m
.4 = (1/2)(9.81) t^2

subtract