Question

You throw a 20.0 g dart horizontally into the side of a small cardboard box of mass 45.0 g that is initially at rest on a tabletop. The coefficient of the kinetic friction between the cardboard box and the tabletop is 0.35. The dart remains stuck in the box, which slides 0.530 m on the tabletop before stopping. How fast did you throw the dart?

Answer 1

let initial speed of dart = u

initial momentum before collision is due to dart

= p1 = 20 u

final momentum of dart and box after collision

= p2 = (20+45)v

as momentum is conserved in collision

p1 = p2

friction opposes the motion of box with negative acceleration of box = 0.35 x 9.8 = 3.43 m/s^2

using

v² - u² = 2 a s

s = stopping distance of box

so v = 1.91 m/s

so p2 = 65 x 1.91

u = 65 x 1.91 / 20 = 6.2 m/s

you should throw with speed = 6.2 m/s

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