## anonymous 5 years ago A car, weighing m kg, and a truck, weighing 4m kg, collide at an angle of A . Initially they are traveling at the same velocity. After the collision they move off together at an angle of B conserving momentum (moves off together). a) Show that tan() = 4 sin A divided by 4 cos A + 1 . b) Show that if their initial velocity is u the velocity that they move off at is v = u/5 sqrt (17 + 8 cos ). c) Find the velocity and direction they move off at if A= pi/2 2 What value of A gives the minimum velocity?

a)from the conservation of LINEAR momentum- $m*\cos o +4m*\cos A =(m+4m)\cos B=5mcos B$ $msin 0+4msin A= 5\sin B$ [above two are get by resolving the momentum into horizontal & perpendicular components ] so,$\tan B= (5\sin B)/(5\cos B)$ $=4msin A/(m+4mcos A)$ $=4\sin A /(1+4\cos A)$