A penny is dropped from a 50 m high bridge, how fast was the penny moving when it hit the water?

See previous post.

To find out how fast the penny was moving when it hit the water, we will use the principles of free fall and the equations of motion.

First, let's determine the time it takes for the penny to fall from the height of the bridge to the water's surface. We can use the equation:

d = (1/2) * g * t^2

Where:
d = distance (50 m)
g = acceleration due to gravity (9.8 m/s^2)
t = time

Rearranging the equation to solve for time (t), we have:

t^2 = (2 * d) / g

t = sqrt((2 * d) / g)

Plugging in the values, we get:

t = sqrt((2 * 50) / 9.8)
t ≈ sqrt(10.2)
t ≈ 3.2 seconds (rounded to one decimal place)

So, it takes approximately 3.2 seconds for the penny to fall from the bridge to the water's surface.

Now, let's determine the penny's final velocity just before it hits the water. We will use the equation:

v = g * t

Where:
v = final velocity
g = acceleration due to gravity (9.8 m/s^2)
t = time (3.2 seconds)

Plugging in the values, we get:

v = 9.8 * 3.2
v ≈ 31.4 m/s (rounded to one decimal place)

Therefore, the penny was moving at a speed of approximately 31.4 m/s when it hit the water.