Try this problem useful for Physics Olympiad based on Relative motion.
The Problem: Relative motion Problem
A 40kg boy is standing on a plank of mass 160Kg. The plank originally at rest, is free to slide on a smooth frozen lake. The boy walks along the plank at a constant speed of 1.5m/s relative to the plank. What is the speed of the boy relative to the ice surface?
Solution:
Let the mass of the boy be (m_b) and that of the plank be (m_p). Let us consider the velocity of the boy with respect to the ice be (v_i), that of the plank with respect to ice be (v_i) and that of the boy with respect to the plank is (v_{bp}).
Now, using conservation of momentum,
$$m_bv_{bi}+(m_pv_{pi})=0$$
$$(40)v_{bi}+(160)v_{pi}=0$$
$$v_{bi}=-4v_{pi}....(i)$$
Also,
$$v_{bi}=v_{bp}+v_{pi}$$
From equation (i),
$$-4v_{pi}=v_{bp}+v_{pi}$$
$$-5v_{pi}=v_{bp}$$
$$v_{pi}=-\frac{1.5}{5}=0.3$$
Hence,
$$v_{bi}=1.2m/s$$
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
Cheenta students shine at the Purple Comet Math Meet 2025 organized by Titu Andreescu and Jonathan Kanewith top national and global ranks.
Celebrate the success of Cheenta students in the Stanford Math Tournament. The Unified Vectors team achieved Top 20 in the Team Round.