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A projectile can have the same range R for two angles of projection. If T and t be the times of flight in the two cases, the product of T and t is (plz give full solution) ......... (a) Directly propotional to square of R.. (b) Directly propotional to R.. (c) Inversely propotional to square of R.. (d) Inversely propotional To R.

A projectile can have the same range R for two angles of projection. If T and t be the times of flight in the two cases, the product of T and t is (plz give full solution) ......... (a) Directly propotional to square of R.. (b) Directly propotional to R.. (c) Inversely propotional to square of R.. (d) Inversely propotional To R.

Grade:12th pass

1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
Dear student,

Range of a projectile is given asR=\dfrac{2u^2sin\theta cos\theta}{g}
If one of the angles is\theta, the other with same range will be90^{\circ}- \theta

HenceT=\dfrac{2usin\theta}{g}
andt=\dfrac{2usin(90^{\circ}-\theta)}{g}=\dfrac{2ucos\theta}{g}

HenceTt=\dfrac{4u^2sin\theta cos\theta}{g^2}\propto R

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