Question

A window is 50cm long. A stone is falling from a height of 40cm above the window. It crosses the window in how many seconds?

Answer 1

The stone will cross the window in approximately 0.20 seconds.

Step-by-step explanation:

To calculate the time it takes for the stone to cross the window, we can use the equation for uniform acceleration:

t = −u + −v / a where t is time, u is initial velocity, v is final velocity, and a is acceleration.

Since the stone is only falling due to gravity and there is no initial vertical velocity (u = 0) or final vertical velocity (v), the equation simplifies to:

t = −v / a

The acceleration due to gravity is approximately -9.8 m/s2, so the stone's final vertical velocity is:

v = √s2 − u2
Using the equation:

v = √s2 − u2

where s is the vertical distance traveled (40 cm) and u is the initial vertical velocity (0 m/s), we get:

v = √(02) − (2 * -9.8 * 0.4)

Therefore, the stone's final vertical velocity is 1.98 m/s. Using the equation for time:

t = −v / a

where v is the final vertical velocity (1.98 m/s) and a is the acceleration due to gravity (-9.8 m/s2),

t = −1.98 / (-9.8)

So the stone crosses the window in approximately 0.20 seconds.