JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Kinematics

Two particles are projected from the same point with the same speed u such that they have the same range R , but different maximum heights,

h_{1}

and

h_{2}

. Which of the following is correct?

Answer: (C)

Solution

Equal range from the same speed means the two launch angles are complementary,

θ

and

9 0^{\circ} - θ

. Their maximum heights are

h_{1} = \frac{u ^{2} s i n ^{2} θ}{2 g}

and

h_{2} = \frac{u ^{2} c o s ^{2} θ}{2 g}

, so

h_{1} h_{2} = \frac{u ^{4} s i n ^{2} θ c o s ^{2} θ}{4 g ^{2}}

. The shared range is

R = \frac{u ^{2} s i n 2 θ}{g} = \frac{2 u ^{2} s i n θ c o s θ}{g}

, so

R^{2} = \frac{4 u ^{4} s i n ^{2} θ c o s ^{2} θ}{g ^{2}} = 16 h_{1} h_{2}

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Single correct option