«
»

Irodov Solutions (1.1-1.3)

This post contains the solutions to the first 3 problems of I.E. Irodov’s “Problems in General Physics”. If you don’t really care about physics, you probably want to ignore this post.

You won’t find the questions here because you need to buy the book to get them, because it would be copyright infringement and because I am lazy to type them out.

1.1

The easiest way to solve this problem is in the reference frame of the raft. With respect to the raft, the boat moves with constant velocity.

Therefore, the entire journey must take 2 hours. Due to this, the flow velocity is given by-

v=\frac{distance}{time}=\frac{6km}{2hr}=3km/hr

1.2

Average velocity for the sections covered with velocities v_{1} and v_{2} is the same as the average of v_{1} and v_{2}, because the point traverses the second half of the distance with these velocities for the same amount of time.

Hence, if the displacement of the particle over the entire journey is 2x then we have-

\langle v \rangle = \frac{distance}{time}=\frac{2x}{\frac{x}{v_{0}}+\frac{2x}{v_{1}+v_{2}}}=\frac{2v_{0}(v_{1}+v_{2})}{2v_{0}+v_{1}+v_{2}}

1.3

The journey can be split into three parts; with the car accelerating in the first part, moving with constant velocity in the second part and decellerating in the last part.

During the first part of the journey, the acceleration a_{1} is 5m/s^{2}. The displacement x_{1} is \frac{1}{2}a_{1}t_{1}^{2}, where t_{1} is the time elapsed. The velocity of the car at the end of the first part is a_{1}t_{1}.

During the second part of the journey, the displacement x_{2} is a_{1}t_{1}t_{2}, where t_{2} is the time elapsed.

The last part of the journey is symmetric to the first, so the displacement(x_{3}) as well as time taken(t_{3}) is the same.

From the information given in the problem, we can construct the following equations-

t_{1}+t_{2}+t_{3}=25\qquad\;\;\implies\quad2t_{1}+t_{2}=25
x_{1}+x_{2}+x_{3}=20\times25\;\implies\;2x_{1}+x_{2}=500

Solving these equations after substituting the expressions for x_{1} and x_{2}, we find that t_{2}=15s.

Tags: ,

This entry was posted on Sunday, November 29th, 2009 at 9:48 pm and is filed under Physics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

2 Responses to “Irodov Solutions (1.1-1.3)”

  1. shashank says:
    December 14, 2009 at 8:18 pm

    can we have complete version of solutions to IE IRODOV general physics

    Reply

Leave a Reply