請教一題物理(動量)

(a) Momentum (動量) in the x-direction = 60 x 5 kg.m/s = 300 kg.m/s
Momentum in the y-direction = 70 x 6 m/s = 420 kg.m/s

Hence, total momentum = square-root[300^2 + 420^2] kg.m/s = 516.1 kg.m/s
By conservation of momentum (動量守恆), momentum after collision
= 516.1 kg.m/s
Velocity after collision = 516.1/(60+70) m/s = 3.97 m/s

Let a be the angle betwwen the final velocity and the x-axis,
tan(a) = 420/300
a = 54.46 degrees

Therefore, the final velocity is 3.97 m/s at direction 54.46 degrees above the x-axis.

(b) Kinetic energy (動能) before collision
= [(1/2).(60).(5^2) + (1/2).(70).(6^)] J = 2010 J
Kinetic energy after collision
= (1/2).(60+70).(3.97^2) J = 1024 J
Hence, kinetic energy loss
= (2010 - 1024) J = 986 J

21a
Ma Ua+Mb Ub=Ma Va+Mb Vb
60*5+70*6=60V+70V
720=130V
V=5.54ms^-1

21b
A的動能損失=(1/2)(60)(5)^2-(1/2)(60)(720/130)^2
A的動能損失=-170J
B的動能損失=(1/2)(70)(6)^2-(1/2)(70)(720/130)^2
B的動能損失=186J
碰撞後動能的總損失=186-170
碰撞後動能的總損失=16J