Paper Ball Motion and Velocity

The video tutorial explores a numerical problem involving air resistance. It begins with a scenario where a crumpled paper ball is dropped from a 25-meter tower. The tutorial calculates the drag coefficient using the terminal velocity concept, derived from the time taken to fall the last 10 meters. It then determines the speed of the paper ball one second after release and calculates the time required to reach a speed of 1 meter per second. The tutorial emphasizes understanding air resistance and terminal velocity through practical calculations.

What is the height of the tower from which the paper ball is dropped?

• 35 meters

• 25 meters

• 45 meters

• 15 meters

How long does it take for the paper ball to fall the last 10 meters?

• 4 seconds

• 5 seconds

• 3 seconds

• 6 seconds

What is the mass of the crumpled paper ball?

• 6 grams

• 5 grams

• 4 grams

• 3 grams

What is the drag coefficient of the crumpled paper ball?

• 0.025

• 0.045

• 0.015

• 0.035

What is the terminal velocity of the paper ball?

• 4 meters per second

• 3 meters per second

• 2 meters per second

• 1 meter per second

What is the speed of the paper ball exactly one second after release?

• 1.987 meters per second

• 2 meters per second

• 1.5 meters per second

• 2.5 meters per second

What is the formula used to calculate the velocity as a function of time?

• v = g * t

• v = b * t / m

• v = m * g / b

• v = v_terminal * (1 - e^(-b/m * t))

How much time does it take for the paper ball to reach a speed of 1 meter per second?

• 0.14 seconds

• 0.44 seconds

• 0.24 seconds

• 0.34 seconds

What is the natural log of 1/2 divided by negative 5 used to calculate?

• Terminal velocity

• Time to reach 1 m/s

• Drag coefficient

• Mass of the paper ball

What happens to the speed of the paper ball as it approaches terminal velocity?

• It remains constant

• It fluctuates

• It decreases

• It increases