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Chilukuri Sai Kartik Grade: 12

What is the relation between Kinetic Energy and Max.Heights?

How to solve these kind of problems;-

Ratio of min.Kinetic energies of two projectiles of same mass is 4:1.REatio of Max.height attained by them is also 4:1.Ratio of their ranges would be?

a)16:1 b)4:1 c)8:1 d)2:1

Plz explain this elaborately.


7 years ago

Answers : (2)

Pratham Ashish
17 Points

if we have a partical with velocity v then
kinetic energy, K = 1/2 m v^2
max height attained by this ,H = v^2 / 2 g
bt inthis case velocity must be vertical , otherwise we have to use its vertical component , v sin x instead of it in the H expression

so , we can easily get , k = mg H ,

problem solution,

let the velocities of two particals be v1, v2
angle with horizontal be x1 ,x2
kinetic energies k1, k2
max. height H1, H2
& range r1 ,r2

k1/k2 = 4 /1 , gives
v1 /v2 = 2/1
we know that,
H1 = (v1sinx1 )^2 /2g
H2 = (v2sinx2 )^2 /2g

so H1 / H2 = 4/ 1
gives v1sinx1 / v2sinx2 = 2/ 1
from eq (1),.............

we get sinx1 = sinx2
so, x1 = x2

range of first r1 = 2v1 sinx cosx / g
second, r2 = 2v2 sinx cosx / g

so, r1/ r2 = v1/ v2 = 2/1

ans is d option.

7 years ago
Pavan kumar
18 Points

The kinetic energies are minimum at the maximum height where velocity is ucosx

Hence 1/2 mu^2cos^2x1= 4*1/2 mv^2cos^2x2

or, ucosx1 = 2vcosx2........(1)

Maximum height is given by H = u^2sin^x/2g

Hence u^2sin^2x1/2g = 4*v^2sin^2x2/2g

or, usinx1 = 2vsinx2.......(2)

(2)/(1) gives tanx1=tanx2 or x1=x2

Using in (1) we get ucosx1 = 2vcosx1

hence u=2v

Therefore R1/R2 = {u^2sin2x1/g}/{v^2sin2x2/g} = (2v)^2sin2x1/v^2sin2x2  = 4

Hence option B is correct.

7 years ago
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