A model rocket is shot straight up and explodes at the top of its trajectory into...

A model rocket is shot straight up and explodes at the top of its trajectory into three pieces as viewed from above and shown in the figure below. The masses of the three pieces are

m_A = 125.0 g,

m_B = 20.0 g,

and

m_C = 30.0 g.

Immediately after the explosion, piece A is traveling at 1.40 m/s, and piece B is traveling at 6.90 m/s in a direction 30° below the negative x axis as shown. What is the velocity of piece C?

magnitude	____m/s
direction	_____° below the positive x axis

Solutions

Expert Solution

fiven

ma = 0.125 kg

mb = 0.02 kg

mc = 0.03 kg

take xaxis as i

y axis as j

z axis as k

from conservation of monentum

total initial momentum = total final momentum

o = mava+mbvb+mcvc

0 = 0.125*1.4(j)+0.02*(6.9cos30(-i)+6.9sin30(-j)+0.03*vc

0 = 0.175 j-0.119i-0.069j+0.03vc

0.03vc = 0.119i-0.106j

vc = 3.97 i-3.53 j

this is the velocity of piece c

magnitude = vc = sqrt(3.97^2+(-3.53)^2) = 5.31 m/s

direction = theta = tan^-1(-3.53/3.97) = 41.64 degrees below the positive x axis

genius_generous answered 1 year ago

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