KinematicsHard
Question
A plane surface is inclined making an angle θ with the horizontal. From the bottom of this inclined plane, a bullet is fired with velocity v. The maximum possible range of the bullet on the inclined plane is
Options
A.
B.
C.
D.
Solution
On the incline plane the maximum possible Range is -
R =
uy = u sin α ux = cos α ax = − g sin β ay = − g cos β
Range = sx = ux T +
ax T2
(on the inclined plane) where T =
⇒ sx = (u cos α)
=
[cos αcos β − sin αsin β]
sx =
[cos (α + β)]
=
[2sinαcos(α + β)]
=
[sin (2α + β) + sin (−β)]
sx =[sin(2α + β) − sin β]
Now sx is max
when sin (2α + β) is max (∵ β = constt)
⇒ 2α + β =
⇒ 
i.e., when ball is projected at the angle bisector of angle formed by inclined plane and dir. of net acceleration reversed.
& (sx)max =
= 
Max. Range on an inclined plane =
Here β = θ ⇒ Rmax =
Ans ″B″
R =
uy = u sin α ux = cos α ax = − g sin β ay = − g cos β
Range = sx = ux T +
ax T2(on the inclined plane) where T =
⇒ sx = (u cos α)
=
[cos αcos β − sin αsin β]sx =
[cos (α + β)]=
[2sinαcos(α + β)]=
[sin (2α + β) + sin (−β)]sx =
[sin(2α + β) − sin β]Now sx is max
when sin (2α + β) is max (∵ β = constt)
⇒ 2α + β =
⇒ i.e., when ball is projected at the angle bisector of angle formed by inclined plane and dir. of net acceleration reversed.
& (sx)max =
= Max. Range on an inclined plane =
Here β = θ ⇒ Rmax =
Ans ″B″Create a free account to view solution
View Solution FreeMore Kinematics Questions
A body of mass 2 kg has an intial velocity of 3 metre/sec along OE and it is subjected to a force of 4 N in a direction ...Which of the following situation is represented by the velocity - time as shown in the diagram : -...When an α-particle of mass ‘m’ moving with velocity ‘v’ bombards on a heavy nucleus of cha...A particle of mass m moves on the axis as follows : it starts from rest at t = 0 from the point x = 0, and comes to rest...An object is thrown horizontally from a point ′A′ from a tower and hits the ground 3s later at B. The line f...