Problem 1.2

Sreepad had gone early to the office today owing to some meetings. Hence, Sanjeev and I were driving down together. This problem was a pretty straight forward one and we solved this independently without much ado.

Solution:
Let the total distance travelled be d. The velocity of travel for the first d/2 km is v₀. Let the time taken be t₀ for this. Hence,

d / 2 = v₀ * t₀
t₀ = d / (2 * v₀)

Now, for the second half of the total distance travelled, the point travelled at v₁ for the first t₁ seconds and at v₂ for the next t₁ seconds. Hence,

d / 2 = v₁ * t₁ + v₂ * t₁
t₁ = d / (2 * (v₁ + v₂))

Average speed = Total Distance / Total Time Taken
Hence,

v_avg = d / (t₀ + t₁ + t₁)
v_avg = d / (d / (2 * v₀) + d / (v₁ + v₂))
v_avg = 1 / (1 / (2 * v₀) + 1 / (v₁ + v₂))
v_avg = 1 / ((2v₀ + v₁ + v₂) / (2 * v₀ * (v₁ + v₂)))
v_avg = (2 * v₀ * (v₁ + v₂)) / (2v₀ + v₁ + v₂)
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Problem 1.1

Today, on our way to the office, there was a huge traffic jam. I had tried solving this problem in the morning but was unsuccessful at it. I related the problem to Sanjeev and Sreepad, who immediately set about solving it. Since there was no paper to work out, Sanjeev started using his visiting cards. Sreepad, started doing it mentally. I had the road to mind, since I was driving, hence I sat and listened to the discussions. Sanjeev was the first one to crack it. Here is the solution.

(I am not giving the complete question here, since that would be some kind of copyright violation. Please buy "Problems in General Physics" by I. E. Irodov for the questions. Believe me, it is going to be money well spent)

Solution:
The trick here is to change the frame of reference. Do not start making equations with earth as the frame of reference. Instead use the river. That is, our frame of reference moves with a velocity equal to the velocity of the river. Suppose the raft is at co-ordinates (0,0,0) at time zero. The boat travels for τ = 60 min and then turns and then travels back to reach the raft. The raft would still be at co-ordinates (0,0,0). Hence it would take exactly 60 min more for the boat to reach the raft. The boat thus takes 120 min or 2τ to reach the raft.

In the mean time the raft has travelled l = 6.0 km. Hence the speed of the river in km/min is,

v = l / 2τ
v = 6 / 2 * 60
v = 1 / 20 km/min

Converting to km/h,

v = 3 km/h
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Part One: Physical Fundamentals of Mechanics

Thought, going about this in a systematic way would be better. I will try to solve from the first problem to the last, one by one. See the next post for the first problem.

Problems in General Physics

This is the well known title of the classic by Igor Evgenyevich Irodov published by Mir Publishers, Moscow. In this blog I will try to solve these problems one by one.

I know that there are umpteen number of "Solutions to Irodov" books and also numerous materials available in the net. But a blog is something I have not found. But again primarily this blog is intended to solve, if not anything, my boredom.

My former batch-mates and current room-mates, Sanjeev Kozhisseri and Sreepad Kutty are assisting me in this venture. Meaning, they are solving problems, which I am not able to.

10 years after junior college and 6 after engineering, my friends and I are finding it a little tough. Mostly because we have forgotten most but the basics. Hopefully, perseverance will see us through.