A particle is projected with a velocity v, so that its range on a horizontal plane is twice the greatest height attained. If g is acceleration due to gravity, then its range is a)4v2/5g b)4g/5v2 c)4v3/5g2 d)4v/5g2Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Range => R = V^2sin2thetha/g

and H = V^2/2g

and given as the relation,

R = 2H

V^2sin2thetha/g = V^2/g

sin2thetha = 1

2thetha = pi/2

or

thetha = pi/4

Therfore the Range becomes =>

R = V^2/g

Answer

Given: A particle is projected with a velocity v, and its range on a horizontal plane is twice the greatest height attained.

To find: Range of the particle.

Solution:

Let's assume that the maximum height attained by the particle is h.

We know that the time taken by the particle to attain the maximum height is given by:

t = u/g, where u is the initial velocity.

Using the equation of motion, we can find the maximum height attained by the particle:

h = u^2/2g

We are given that the range of the particle is twice the maximum height attained. Therefore, we can write:

R = 2h = 2u^2/2g = u^2/g

We know that u = v (initial velocity), therefore:

R = v^2/g

The range of the particle is given by the formula:

R = v^2*sin(2θ)/g

Where θ is the angle of projection.

We know that the particle is projected horizontally, which means that θ = 0.

Therefore, sin(2θ) = 0, and the range of the particle is given by:

R = v^2/g

Substituting the value of R, we get:

Range = 4v^2/5g

Hence, the correct answer is option A.

Note: The formula for the range of a projectile is R = u^2*sin(2θ)/g, where u is the initial velocity and θ is the angle of projection. In this case, since the particle is projected horizontally, the angle of projection is 0, and sin(2θ) becomes 0.

Answer

Answer

Easy problem option 'a' is correct. But if i give you the straight solution then i will be impossible for you to learn anything. So, i am advising you to hold rough paper and pen and solve the ques how i am telling you. First remember or find formulas of range and max. height, then uquate them according to the qiestion R = 2H. After cutting of some common terms you will find tan(theta)= 2, by traingle T-rules find sin and cos then place their values in range's formula. You will have the same result as in option 'a'.

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