A window is 1.50m high. A stone falling from above passes the top of the window with a speed of 3m/s. When will it pass the bottom of the window?

x = x0 + v0*t + 1/2*a*t^2

x0=1.5 v0=-3 a=-10 (or something close, depending on what you're told to use in your class).

You want the time for when x=0 (where 0m = the bottom of the window).

0 = 1.5 - 3 x t - 5 x t^2

1.5 = 3xt + 5xt^2

0=5t^2 +3t -1.5

You use the quadratic equation and you find : t ~= 0.3245

To find out when the stone will pass the bottom of the window, we need to calculate the time it takes for the stone to fall from the top to the bottom of the window.

Let's use the kinematic equation, which relates displacement, initial velocity, time, and acceleration:

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

Where:
s = displacement (height of the window) = 1.50m
u = initial velocity = 3m/s (speed of the stone)
a = acceleration = 9.8 m/s^2 (acceleration due to gravity)
t = time taken

At the top of the window, the stone is moving downwards, so its initial velocity is negative (-3m/s).

Plugging in the values:

1.50 = (-3)t + (1/2)(-9.8)t^2

Rearranging and simplifying the equation:

4.9t^2 - 3t - 1.50 = 0

To solve this quadratic equation, we can either use the quadratic formula or factorize it.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, a = 4.9, b = -3, and c = -1.50.

t = (-(-3) ± √((-3)^2 - 4(4.9)(-1.50))) / (2(4.9))

Simplifying further:

t = (3 ± √(9 + 29.4)) / 9.8

t = (3 ± √38.4) / 9.8

Now we can calculate the two possible values for t:

t1 = (3 + √38.4) / 9.8
t2 = (3 - √38.4) / 9.8

Calculating the values using a calculator:

t1 ≈ 1.036 seconds
t2 ≈ -0.211 seconds

Since time cannot be negative, we disregard t2.

Therefore, the stone will pass the bottom of the window approximately 1.036 seconds after passing the top of the window.

To determine when the stone will pass the bottom of the window, we need to calculate the time it takes for the stone to fall from the top to the bottom of the window. We can do this by using the formula for the time it takes for an object to fall a certain distance.

The formula for calculating the time it takes for an object to fall a certain distance is:

t = √(2h/g)

Where:
t = time (in seconds)
h = height (in meters)
g = acceleration due to gravity (approximately 9.8 m/s²)

In this case, the height (h) is equal to the height of the window, which is 1.50 meters. So, let's plug in the values and calculate the time it takes for the stone to fall from the top to the bottom of the window.

t = √(2 * 1.50 / 9.8)
t = √(3 / 9.8)
t ≈ 0.55 seconds

Therefore, it will take approximately 0.55 seconds for the stone to pass the bottom of the window after passing the top of the window.