Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R . If A and B reached the maximum height \(\mathrm{h}_{1}\) and \(\mathrm{h}_{2}\) respectively, then \(\mathrm{R}=4 \sqrt{\mathrm{~h}_{1} \mathrm{~h}_{2}}\) Reason R: Product of said heights. \(\mathrm{h}_{1} \mathrm{~h}_{2}=\left(\frac{\mathrm{u}^{2} \sin ^{2} \theta}{2 \mathrm{~g}}\right) \cdot\left(\frac{\mathrm{u}^{2} \cos ^{2} \theta}{2 \mathrm{~g}}\right)\) Choose the CORRECT answer :

(A) Both A and R are true and R is the correct explanation of A .

(B) Both A and R are true but R is NOT the correct explanation of A .

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Kinematics

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R . If A and B reached the maximum height

h_{1}

and

h_{2}

respectively, then

R = 4 h_{1} h_{2}

Reason R: Product of said heights.

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

Choose the CORRECT answer :

(A)Both A and R are true and R is the correct explanation of A .✓ Correct
(B)Both A and R are true but R is NOT the correct explanation of A .
(C)A is true but R is false
(D)A is false but R is true

Answer: (A)

Solution

For projectiles with the same range, the angles satisfy

θ_{1} + θ_{2} = 9 0^{\circ}

. The maximum heights are

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

and

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

. Their product is

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

, since range

R = \frac{u ^{2} s i n 2 θ _{1}}{g}

. Therefore

R = 4 h_{1} h_{2}

. Both Assertion and Reason are true, and R correctly explains A.

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Single correct option

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JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Kinematics

Solution

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