an object is thrown by making an angle 60 degree to the horizontal if it hits the vertical wall of a height H by making an angle 30 degree with the horizontal then the relation between height H an initial velocity u is....
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Class 11
>>Physics
>>Motion in a Plane
>>Projectile Motion
>>A particle at a height ' h ...
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A particle at a height 'h' from the ground is projected with an angle 30
∘
from the horizontal, it strikes the ground making angle 45
∘
with horizontal. It is again projected from the same point at height h with the same speed but with an angle of 60
∘
with horizontal. Find the angle it makes with the horizontal when it strikes the ground:
Hard
Solution
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Correct option is
C
tan
−1
(
5
)
In first case, Let initial velocity be u the initial velocity in horizontal direction is ucos30
o
, in vertical direction is usin30
o
.
As final angle when hitting ground is 45
o
, so final velocity in vertical direction is equal in magnitude to final velocity in horizontal direction, ucos30
o
.
Using the formula, v
2
−u
2
=2as, in vertical direction,
(−ucos30
o
)
2
−(usin30
o
)
2
=2gh
⇒u=2
gh
In second case, Let final velocity in vertical direction be v
1
. the initial velocity in horizontal direction is ucos60
o
, in vertical direction is usin60
o
=2
gh
×0.5=
gh
.
Using the formula, v
2
−u
2
=2as, in vertical direction,
(v
1
)
2
−(usin60
o
)
2
=2gh
⇒v
1
=
5gh
So the final angle is, tan
−1
(
gh
5gh
)=tan
−1
5