Question

Two particles A and B are projected from the same point with the same speed but at different angles a and B with the horizontal, such that the maximum height of A is (2/3)rd of the horizontal range of B. Then which of the following relations are true​

Answer 1

Answer:

sorry friend

Explanation:

i dont know the answer

Answer 2

Two particles A and B are projected from the same point with the same velocity of projection but at different angles α and β of projection, such that the maximum height of A is two-thirds of the horizontal range of B. then which of the following relations are true?

A. range of  A= maximum height of B

B.  3(1-cos2α)=8sin2β

C. the maximum value of β is  sin-1(3/4)

D. maximum horizontal range of A = u 2 / g and this occurs when β = (1/2)*sin − 1 ( 3/8 )

options B and D are correct.

Given:

Two particles A and B are projected with the same velocity

projection angle of A is α.

projection angle of B is β

Hmax of A = (2/3) x Range of B

To Find:

The relations which are true.

Solution:

From the given statement, Hmax of A = (2/3) x Range of B

we know, Hmax = u²sin²α/2g

                Rb = u²sin2β/g

∴ u²sin²α/2g = 2u²sin2β/3g

sin²α = 4/3 x sin2β --------(2)

(1 - cos2α)/2 = 4/3 *2sinβcosβ

∴ 3(1-cos2α)=8sin2β --------(1)

Hence, relation b is correct.

From equation (1), βmax = 1/2*sin⁻¹(3/8).

Hence, relation c is incorrect.

Now substitute βmax in (2)

we get, α = 45° substitute in the range of A

Ra = u²sin2α/2g

     =  u²sin2(45°)/g

     =  u²sin90°/g

     =  u²/g                    (∵ sin 90° = 1)

Hence, relation D is correct.

Therefore, relations B and D are correct.

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