Ncert Exercises & Solutions

A particle slides down a frictionless parabolic track starting from rest at point $A$. Point $B$ is at the vertex of the parabola and point $C$ is at a height less than that of point $A$. After $C$, the particle moves freely in the air as a projectile. If the particle reaches the highest point at $P$, then,

1.	kinetic energy at $P$ = kinetic energy at $B$
2.	height at $P$ = height at $A$
3.	total energy at $P$ = total energy at $A$
4.	time of travel from $A$ to $B$ = time of travel from $B$ to $P$

Step 1: Find the total energy of the particle.

As the given track y = x is a frictionless track thus, total energy (KE+ PE) will be the same throughout the journey.

Hence, total energy at A = Total energy at P. At B, the particle is having only KE but at P some KE is converted to P

Hence, $(K E)_{\cdot B} > (K E)_{ρ}$

Total energy at A = PE= Total energy at B= KE

= Total energy at P
= PE+ KE

Step 2: Find the potential energy of the particle at different points.

The potential energy at A, is converted to KE and PE at P, hence
(PE) P< (PE) A
Hence, (Height) P< (Height) A

As, the height of P < Height of A
Hence, path length AB > path length BP
Hence, the time of travel from A to B $\neq$ Time of travel from B to P.

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1.	kinetic energy at \(P\) = kinetic energy at \(B\)
2.	height at \(P\) = height at \(A\)
3.	total energy at \(P\) = total energy at \(A\)
4.	time of travel from \(A\) to \(B\) = time of travel from \(B\) to \(P\)