5. A 1000 kg motorboat travelling due West strikes a 5000 kg ship traveling at 1

Question

5. A 1000 kg motorboat travelling due West strikes a 5000 kg ship traveling at 1 m/s due North. Immediately after the collision the speed of the two vessels combined is 1.25 m/s. What was the speed of the motorboat before the collision? i) What was the Northern component of moments of the ship before collision? ii) What was the Northern component of momentum of the boat before collision? iii) What was the Northern component of the total momentum before collision? iv) What is the Northern component of the momentum of the collided vessels after collision? v) What is the Northern component of the velocity of the collided vessels after collision? vi) What is the Western component or the velocity of the collided vessels after collision? vii) What is the Western component of the momentum of the collided vessels after collision? viii) What is the Western component of the ship before collision? ix) What is the Western component of the boat before collision? x) What is the speed of the motorboat before the collision? xi) What is the direction of the momentum of the collided vessels collision?

Explanation / Answer

for full credit

i = east          -i = west

j = north         -j = south

v1 = v1xi

v2 = v2yj

v = vi + vyj

v = sqrt(V^2+Vy^2)

from momentum conservation

initial momentum = final momentum

m1*v1 + m2*v2 = (m1+m2)*V

-(1000*v1xi) + (5000*1)j = 6000*(Vxi + Vyj)

comparing i

-1000*v1x = 6000*Vx

V1x = -6*Vx .(1)

comparing j

5000 = 6000*Vy

Vy = 5/6 ............ .(2)

given V = 1.25

sqrt(vx^2 + Vy^2) = 1.25

Vx^2 + Vy^2 = 1.5625

Vx^2 + (5/6)^2 = 1.5625

Vx = 0.932 m/s

from 1

V1x = -6*Vx = -5.592 m/s

so speed of motor boat = 5.592 m/s

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