A 15kg object is shot 30 degrees above the horizontal at 20m/s. When the object is at the top of its flight path, it has a perfectly inelastic collision with a 5kg object going 10m/s in the negative y-direction. What is the total displacement in the x-direction from the objects initial position? (As much details as possible in the solution please! (: I know this is an energy, collision and projectile motion problem.)
Let M be the mass of object 1 = 15 kg
be the angle = 300
u be the initial velocity of object 1 = 20 m/s
h be the maximum height of object 1
d be the net displacement
d1 be the displacemet from A to B
d2 be the displacement from B to C
d = d1 + d2
m be the mass of object 2 which collide with object 1 = 5 kg
(M+m) is the mass of object 3 (After collision of object 1 and object 2) = 20 kg
Let the horizontal velocity of object 1 before collision be uMx
and the vertical velocity of object 1 before collision be uMy
During Projectile motion at maximum height there will be only horizontal component of velocity
so
uMx = ucos() = 17.321 m\s
uMy = 0
Let the horizontal velocity of object 1 before collision be umx = 0m/s
the vertical velocity of object 1 before collision be umy = 10 m/s
Let the horizontal velocity of object 3 before collision be vx
and the vertical velocity of object 1 before collision be vy
By conservation of Momentum in horizontal direction at maximum height of object 1
By conservation of Momentum in vertical direction at maximum height of object 1
Let v be the Net velocity of object 3 just after collision
Maximum height of object 1
The displacement from A to B
Let t be time taken by object 3 to reach from maximum height to point C
Net displacement will be
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