A mining cart is pulled up a hill at 20 km / h and then pulled back down the hill at 35 km / h

Name: Problem 85, Chapter 2: Fundamentals of Physics
Uploaded: 2021-07-20T13:28:28-08:00
Duration: 1 min 1 s
Channel: Donald Albin
Description: A mining cart is pulled up a hill at 20 km / h and then pulled back down the hill at 35 km / h through its original level. (The time required for the cart's reversal at the top of its climb is negligible.) What is the average speed of the cart for its round trip, from its original level back to its original level?

step 1 All right. I did all of this using some complicated method of fractions of times and whatever. B

Question

A mining cart is pulled up a hill at $20 \mathrm{~km} / \mathrm{h}$ and then pulled back down the hill at $35 \mathrm{~km} / \mathrm{h}$ through its original level. (The time required for the cart's reversal at the top of its climb is negligible.) What is the average speed of the cart for its round trip, from its original level back to its original level?

   A mining cart is pulled up a hill at $20 \mathrm{~km} / \mathrm{h}$ and then pulled back down the hill at $35 \mathrm{~km} / \mathrm{h}$ through its original level. (The time required for the cart's reversal at the top of its climb is negligible.) What is the average speed of the cart for its round trip, from its original level back to its original level?

Fundamentals of Physics

David Halliday,… 11th Edition

Chapter 2, Problem 85

Instant Answer

Solved by Expert Donald Albin

07/20/2021

Step 1

1 km/h = (1000 m/km) / (3600 s/h) = 5/18 m/s So, 20 km/h = (20 * 5/18) m/s = 50/9 m/s And, 35 km/h = (35 * 5/18) m/s = 175/18 m/s Let's assume the distance up the hill is d meters. Time taken to go up the hill = distance / speed = d / (50/9) = 9d/50 Time Show more…

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A mining cart is pulled up a hill at $20 \mathrm{~km} / \mathrm{h}$ and then pulled back down the hill at $35 \mathrm{~km} / \mathrm{h}$ through its original level. (The time required for the cart's reversal at the top of its climb is negligible.) What is the average speed of the cart for its round trip, from its original level back to its original level?

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Key Concepts

Average Speed

Average speed is defined as the total distance traveled divided by the total time taken. It is a fundamental concept in kinematics that provides a measure of the overall rate of motion over a journey, regardless of variations in speed during different segments of the trip.

Time Calculation

Calculating the time for each segment of a journey is based on the relationship time = distance/speed. This key step allows for the determination of the total time taken when different speeds are involved in different segments of the same trip.

Harmonic Mean for Equal Distance Segments

When a journey is divided into two segments of equal distance covered at different speeds, the average speed for the entire journey is best determined using the harmonic mean rather than the arithmetic mean. The harmonic mean effectively balances the contributions of each segment by considering the reciprocal of the speeds.

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