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
Question
Answer:
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 .