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

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