A penny is dropped from a 300ft high bridge.

a. How long does it take for the penny to reach the ground below?

b. What is the velocity of the penny upon impact?

That's what I want to know.

100

To determine how long it takes for the penny to reach the ground and its velocity upon impact, we can use the equations of motion. Assuming the only force acting on the penny is gravity, we can use the kinematic equation:

1. For the time taken (a):
The equation to find the time taken for an object to fall freely from a height h is given by:
h = 1/2 * g * t^2
where:
h = height (300ft in this case)
g = acceleration due to gravity (32.2 ft/s^2)

Rearranging the equation, we have:
t = sqrt(2h/g)

Substituting the given values:
t = sqrt(2 * 300ft / 32.2 ft/s^2)

Simplifying gives us the time taken for the penny to reach the ground.

2. For the velocity upon impact (b):
The equation to find the final velocity of an object after falling freely from a height h is given by:
v = sqrt(2gh)
where:
v = final velocity
h = height (300ft in this case)
g = acceleration due to gravity (32.2 ft/s^2)

Substituting the given values:
v = sqrt(2 * 32.2 ft/s^2 * 300ft)

Simplifying gives us the velocity at the moment of impact.

To answer these questions, we can use the laws of motion and the principles of kinematics. Let's break it down step by step.

a. How long does it take for the penny to reach the ground below?

To calculate the time it takes for the penny to fall, we can use the kinematic equation:

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

Where:
- s is the distance (height) the penny falls (300ft)
- u is the initial velocity of the penny (0ft/s, as it is dropped from rest)
- a is the acceleration due to gravity (-32.2ft/s^2, assuming it is on Earth)
- t is the time we're trying to find

Since we are interested in finding the time, we want to rearrange the equation:

s = ut + (1/2)at^2
300ft = (0ft/s)t + (1/2)(-32.2ft/s^2)t^2

Simplifying the equation, we get:

300ft = -(16.1ft/s^2)t^2

Now we can solve for t:

t = sqrt(300ft / -16.1ft/s^2)
t ≈ 3.07 seconds

Therefore, it takes approximately 3.07 seconds for the penny to reach the ground below.

b. What is the velocity of the penny upon impact?

To calculate the velocity of the penny upon impact, we can use another kinematic equation:

v = u + at

Where:
- v is the final velocity upon impact
- u is the initial velocity (0ft/s)
- a is the acceleration due to gravity (-32.2ft/s^2, assuming it is on Earth)
- t is the time (3.07 seconds, as found in part a)

Substituting the given values into the equation, we get:

v = 0ft/s + (-32.2ft/s^2)(3.07s)
v ≈ -98.77ft/s

The negative sign indicates that the velocity is directed downward, pointing towards the ground. Therefore, the velocity of the penny upon impact is approximately 98.77ft/s downward.