A vehicle is moving with constant acceleration kg up a slope of inclination 
, the floor of the vehicle being parallel to the slope. Show that if a particle is falling freely inside the vehicle its acceleration relative to the vehicle makes an angle 
with the floor, where
c ot 
= k sec 
+ tan 
A particle is projected inside the vehicle from a point A on the floor, its initial velocity relative to the vehicle being V at an angle 
(> 
) with the floor, as shown in the diagram. It strikes the ceiling at B, where AB is perpendicular the floor and AB = h. By considering motion parallel to the slope, show that the time of flight is 
and deduce that
h = 
.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Acceleration of particle with respect to trolley 
= 
– 
φ = 180 – [90 + α + β ]
= 90 – ( α + β )
= 
= 
= 
k sin β = cos ( α + β )
k sin β = cos α cos β – sin α sin β
k cos α + tan α = cot β ….. (i)
(a x ) PT = – [g sin α + kg]
with respect to observer in trolley (vehicle)
x PT = (u x ) Pt t + 
0 = v cos θ T – 
(g sin α + kg) T 2
T = 
…………(ii)
From (i)
k + sin α = cot β cos α
Putting in (ii)
T = 
In y–direction:
Y PT = (u y ) PT t + 
(a y ) PT t 2 h = v sinq T – 
g cos α T
2
h = T 
h = 
h = 
h = 
h = 
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