help me please! with full work shown In the figure, a 2.1 kg box of running shoe

Question

help me please! with full work shown

In the figure, a 2.1 kg box of running shoes slides on a horizontal frictionless table and collides with a 1.5 kg box of ballet slippers initially at rest on the edge of the table, at height h = 0.73 m. The speed of the 2.1 kg box is 3.0 m/s just before the collision. If the two boxes stick together because of packing tape on their sides, what is the magnitude of their velocity just before they strike the floor? Use 2 different methods and see if you get the same result.

Explanation / Answer

according to energy conservation

after sticking together at the top point

(m1*v1^2)/2 = [(m1+m2)*v2^2]/2

=> (2.1*3^2)/2 = [(2.1+1.5)*v2^2]/2

=> v2 =Vx= 2.29 m/s in horizontal direction

it will remain same in horizontal direction just before striking the floor

vertical velocity Vy = (2*gh)^0.5 = (2*9.8*0.73)^0.5 = 3.78 m/s

SO net velocity V = [2.29^2 + 3.78^2]^0.5 = 4.41 m/s

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