Question
At what angle should a ball be projected up an inclined plane with a velocity so that it may hit the incline normally. The angle of the inclined plane with the horizontal is α.
Answer: Option B
:
B
As the ballhas to hit the inclined plane normally, so in that position the x-component of velocity will be zero and velocity will have y-component only.
The ball will hit the incline normally if its parallel component of velocity reduces to zero during the time of flight.
By analyzing this motion along incline, i.e., x-direction vx=ux+axt
Here vx=0,ux=v0cosθ,ax=−gsinα
0=vocosθ−(gsinα)T⇒T=vocosθgsinα ........(i)
Also the displacement of the particle in y-direction will be zero. Using
y=uyt+12ayt2⇒0=vosinθ.T−12gcosα.T2
This gives T = 2vosinθgcosα ...............(ii)
From (i) and (ii), we have vocosθgsinα=2vosinθgcosα⇒cosθsinα=2sinθcosα⇒2tanθtanα=1⇒tanθ=[12cosα]
⇒=tan−1(12cotα) which is the required angle of projection.
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:
B
As the ballhas to hit the inclined plane normally, so in that position the x-component of velocity will be zero and velocity will have y-component only.
The ball will hit the incline normally if its parallel component of velocity reduces to zero during the time of flight.
By analyzing this motion along incline, i.e., x-direction vx=ux+axt
Here vx=0,ux=v0cosθ,ax=−gsinα
0=vocosθ−(gsinα)T⇒T=vocosθgsinα ........(i)
Also the displacement of the particle in y-direction will be zero. Using
y=uyt+12ayt2⇒0=vosinθ.T−12gcosα.T2
This gives T = 2vosinθgcosα ...............(ii)
From (i) and (ii), we have vocosθgsinα=2vosinθgcosα⇒cosθsinα=2sinθcosα⇒2tanθtanα=1⇒tanθ=[12cosα]
⇒=tan−1(12cotα) which is the required angle of projection.
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