Find out the common velocity, Mechanical Engineering

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Find out their common velocity:

An aeroplane weighing 40 kN horizontally moves with a velocity of 20 m/sec (72 kmph, that means 72 km per hour). A helicopter of weight 20 kN is proceeding at 30 m/sec (108 kmph) towards North in the same horizontal plane & collides with aeroplane. If the two masses get entangled after collision, find out their common velocity.

Solution

As momentum is a vector along the direction of the velocity of the mass, while the momenta M1 and M2 of the aeroplane and the helicopter, respectively, are along two different directions of the two masses, vector rules have to be adopted to determine its resultant momentum.

1 =(Momentum of aeroplane before collision in units (kg m/sec) along  589_Find out their common velocity.png)

= (40 × 20 )/ g  × 1000

2  =  (Momentum of helicopter before collision along1828_Find out their common velocity1.pngin (kg m/sec))

= (20 × 30)/ g  × 1000

The combined mass = (60 × 1000)/ g    kg

 

Therefore, if M c is the resultant momentum along direction796_Find out their common velocity2.png at ∠ α with OA then

V¯c is the common velocity along 796_Find out their common velocity2.png

                                                  ∴ M¯ c  = M¯1 + M¯ 2

1000 × (60/g) V¯c = [(40  × 20 )/g +( 20 × 30)/g (OB ↑)]× 1000

This is a vector addition,

714_Find out their common velocity3.png

∴ Vc  = 100 /6= 16.67 m / sec along OR

where,

tan α = AR/ OA  = 600 /800 = 0.75

∴          α = 36o.87


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