Kinematics

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Question 233 of 308

Two objects are projected with same velocity uu however at different angles α\alpha and β\beta with the horizontal. If α+β=90∘\alpha +\beta =90^{\circ}, the ratio of horizontal range of the first object to the 2nd{2}^{nd} object will be :

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Answer: (D) 1:11:1

Given: α+β=90∘\alpha +\beta =90^{\circ}
Range of the first projectile:
R1=u2sin⁡2αg{R}_{1}=\dfrac{{u}^{2}\sin 2\alpha }{g}
Range of the second projectile:
R2=u2sin⁡2βg=u2sin⁡(180∘−2α)g=u2sin⁡2αg{R}_{2}=\dfrac{{u}^{2}\sin 2\beta }{g} =\dfrac{{u}^{2}\sin (180^{\circ}-2\alpha )}{g} =\dfrac{{u}^{2}\sin 2\alpha }{g}
As we can see, both are equal.
R1=R2{R}_{1}={R}_{2}
Therefore,
R1:R2=1:1{R}_{1}:{R}_{2}=1:1

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