A stone is projected with the same velocity at 22030',67030' to the horizontal then the ratio of ranges is A)1:1 b)1:3 c)3:1 d)root over 2:1 (with proper steps please)
Answers
When a projectile is projected with a velocity, u and at angle, θ to the horizontal, the maximum height reached by the projectile is given by,
H=
2g
u
2
sin
2
θ
As both projectiles have same projected velocity, so
H∝sin
2
θ
Thus ratio of maximum heights
H
60
H
30
=
sin
2
60
sin
2
30
=
3/4
1/4
=1/3
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Class 11
>>Physics
>>Motion in a Plane
>>Projectile Motion
>>Two projectiles are projected with the s
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Two projectiles are projected with the same velocity. If one is projected at an angle of 30
o
and the other at 60
o
to the horizontal. The ratio of maximum heights reached, is
Medium
Solution
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Correct option is A)
When a projectile is projected with a velocity, u and at angle, θ to the horizontal, the maximum height reached by the projectile is given by,
H=
2g
u
2
sin
2
θ
As both projectiles have same projected velocity, so
H∝sin
2
θ
Thus ratio of maximum heights
H
60
H
30
=
sin
2
60
sin
2
30
=
3/4
1/4
=1/3