Two bodies are projected at an angles of 045 and 060 with the horizontal with samevelocity simultarieously. The ratio of their horizontal ranges is
Question
Two bodies are projected at an angles of 045 and 060 with the horizontal with same velocity simultarieously. The ratio of their horizontal ranges is
Solution
The horizontal range (R) of a projectile launched with an initial velocity (u) at an angle (θ) with the horizontal is given by the equation:
R = (u²/g) * sin(2θ)
where g is the acceleration due to gravity.
Given that the two bodies are projected with the same velocity, the ratio of their horizontal ranges R1/R2 is given by:
R1/R2 = sin(2θ1) / sin(2θ2)
Substituting the given angles into the equation:
R1/R2 = sin(245°) / sin(260°)
R1/R2 = sin(90°) / sin(120°)
Since sin(90°) = 1 and sin(120°) = √3/2,
R1/R2 = (1) / (√3/2) = 2/√3
Therefore, the ratio of their horizontal ranges is 2/√3.
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