Question

An object of mass

m = 6.7 g is fired into a larger object of mass M = 305 g that was initially at rest at the edge of a table. The smaller object becomes embedded in the larger object and the combined object lands on the floor a distance of 2.0 m away from the table. If the tabletop is 1.0 m above the floor, determine the initial speed of the smaller object in m/s.

Answer #1

Sol:

Given

m= 6.7 kg

M=305 kg

d=2 m

h=1 m

Total mass(mt)=311.7 g

vertically using equation of motion

s = ut + ½at²

u = initial vertical velocity = 0 (combined mass falls off table)

h = 0 + ½at²

1 = ½gt²

or

t² = 2 / 9.81

= 0.204

t = 0.452 s

therefore the combined mass initial horizontal velocity which is constant = v

=> vt = 2 m

0.452v = 2

v = 2/0.452

= 4.424 m/s

if the initial velocity of the 6.7 g mass = u

And using conservation of momentum horizontally,we get

=> 6.7*u + 305(0) = 311.7v

u = 311.7*(4.424) / 6.7

= 205.81 m/s

Hope this helps you..

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