In a shipping company distribution center, an open cart of mass 50 kg is rolling to the left at a speed of 5 m/s. You can ignore friction between the cart and the floor. A 15 kg package slides down a chute that makes an angle of 27 degrees below the horizontal. The package leaves the chute with a speed of 3 m/s, and lands in the cart after falling for 0.75 seconds. The package comes to a stop in the cart after 4 seconds. What is:a) the speed of the package just before it lands in the cart

Explanation:

The package leaves the chute with a speed of 3 m/s, and lands in the cart after falling for 0.75 seconds . During .75 second duration . package undergoes free fall due to which additional vertical velocity is added

velocity added = a x t

= 9.8 x .75

= 7.35 m /s

Total vertical velocity

= 3 sin27 + 7.35

= 8.71 m /s

Horizontal component = 3 cos 27

= 2.67 m /s

If v be the resultant velocity of these components

v² = 2.67² + 8.71²

v² = 7.13 + 75.86

v = 9.11 m /s .

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