A body of mass m is projected from ground with
speed u at an angle Theta with horizontal then find
aut :-
1) Initial velocity vector
2) Velocity vector at topmost point
3) velocity vector when body Strikes on ground
4) Change in momentum between point of projection and striking point
on ground.
Answers
Explanation:
A body of mass m is projected from ground with
A body of mass m is projected from ground withspeed u at an angle Theta with horizontal then
Let theta = x,
1) Initial velocity vector = u sinx i + u cosx j
2) Velocity vector at topmost point = 0 i + u cos j
3) velocity vector when body Strikes on ground = u sinx i + u cosx (-j)
4) Change in momentum between point of projection and striking point
4) Change in momentum between point of projection and striking pointon ground = m ( v final -v initial) =| m( 2 u cosx) |
initial speed = u
angle = theta
1)
We know
x component of a vector U= ucos\thetaθ
y component of vector U= usin\thetaθ
Uvector= \pink{(u \cos\theta \: ) i + (u \sin \theta )j}(ucosθ)i+(usinθ)j -----i
━━━━━━━━━━━━━━━
2.
Now clearly from the diagram,
Vvector=
\pink{(u \: cos \theta) i - (u \: sin \: \theta) j}(ucosθ)i−(usinθ)j ----ii
━━━━━━━━━━━━━━━
3.
At the top,
the vertical velocity will be zero or Uy=0
thus at top,
Vvector
= (Ux)i +(Uy)j
=(Ux)i
=\blue{(u \: cos \: \theta) i}(ucosθ)i
━━━━━━━━━━━━━━━━
4.
Momentum:
=m (Vfinal- Vinitial) [from equation i and ii]
=\red{m( - 2u \: sin \: \theta) j}m(−2usinθ)j