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