Question

Figure shows a particle sliding on a frictionless track which terminates in a straight horizontal section. If the particle starts slipping from the point A, how far away from the track will the particle hit the ground?
Concept of Physics - 1 , HC VERMA , Chapter " Work and Energy"

Answer 1

Given in the equation :-
The particle descends through the point of termination :- h
h = 1.0 -0.5 
h= 0.5 m.
Initial Kinetic Energy = 0
So according to the condition, The point of termination of Track so it's Kinetic energy is due to change in potential energy.


Kinetic Energy = (1/2) mv² .
Change in potential energy = mgh .
Equating both.
(1/2)mv² = mgh
v² /2 = gh
v² = 2gh
v = √2gh
v = √(2 × 9.8 × 0.5 )
v = √9.8
v = 3.1304 m/s

Now from the formula as here the particle is travelling in the parabolic medium so , u =0
s = ut + 1/2(gt²)
0.5 = 0 + (1/2) 9.8 × t²
t² = (0.5 × 2)/9.8
t² = 1/9.8
t² = 0.1020
t = 0.32 s.

So now the distance travelled ,
speed × time 
= 3.13 × 0.32 
= 1 m. 

Hence the particle hit the ground 1 m from the track.


Hope it Helps.

Answer 2

Hope this is easier.