How to Find the Velocity When the Coin Strikes the Ground

TL;DR

Calculate position, velocity, average velocity, time to reach ground, and impact velocity of a free-falling object.

Transcript

okay so we have a ward problem a silver dollar is dropped from the top of a building that is 1370 feet tall let's go ahead and draw a little picture of the building so here's our building and it is 1370 feet tall let's say 3. use the position function below for free falling objects and then it says determine the position and velocity functions for ... Read More

Key Insights

• 🥰 Initial velocity (v naught) and initial position (s naught) are crucial in solving free-falling object problems.
• 🧘 Derivative of the position function yields the velocity function for the object.
• 🧘 Average velocity is determined by the change in position over a specified time interval.

Questions & Answers

Q: How do you calculate the position and velocity functions of a free-falling object?

To calculate the position function, use the formula s(t) = -16t^2 + 1370, where t is time. The velocity function is the derivative of the position function, v(t) = -32t.

Q: What is the formula for average velocity and how is it calculated?

The formula for average velocity is (s(b) - s(a)) / (b - a), where s is the position function. Substitute the values of a = 3 and b = 4 to find the average velocity in the specified interval.

Q: How do you find the time required for the coin to reach the ground?

Set the position function, -16t^2 + 1370, equal to zero and solve for t. The positive root gives the time taken for the coin to reach the ground, which is approximately 9.253 seconds.

Q: What is the impact velocity of the coin when it hits the ground?

To find the impact velocity, substitute the time taken to reach the ground (9.253 seconds) into the velocity function v(t) = -32t. The impact velocity of the coin is -296.096 feet per second.

Summary & Key Takeaways

• A silver dollar is dropped from a 1370-foot tall building.

• Calculate position and velocity functions using the given formula.

• Determine average velocity, time to reach the ground, and impact velocity of the falling coin.