Constants I Periodic Table Two cars, both of mass m, collide and stick together.
ID: 2035489 • Letter: C
Question
Constants I Periodic Table Two cars, both of mass m, collide and stick together. Prior to the collision, one car had been traveling north at speed 3u, while the second was traveling at speed 20 at an angle ? south of east (as indicated in the figure). After the collision the two-car system travels at speed Vfinal at an angle 8 east of north. (Figure 1) Find the speed vfimnl of the joined cars after the collision Express your answer in terms of u and ? View Available Hint(s) a3.25-3sino Correct Figure 1 or t Part B What is the angle 8 with respect to north made by the velocity vector of the two cars after the collision? Express your answer in terms of ?. Your answer should contain an inverse trigonometric function using the notation asin, atan etc. and not arcsin, arctan etc. View Available Hint(s)Explanation / Answer
given two cars, both mass m, collide and stick together
prior to collision
car 1, speed = 3v along north direction
car 2, speed = 2v along phi south of east
after collision, angle is theta east of north
a. let thefinal speed be v'
then
from conservation of moemntum
m*2v*cos(phi) = 2m*v'*sin(theta)
also
m*3v - m*2v*sin(phi) = 2m*v'*cos(theta)
hence
2vcos(phi) = 2v'*sin(theta)
3v - 2vsin(phi) = 2v'*cos(phi)
squaring and adding
4v^2cos^2(phi) + 9v^2 + 4v^2sin^2(phi) - 12v^2*sin(phi) = 4v'^2
v' = v*sqroot(3.25 - 3*sin(phi))
b. sin(theta) = v*cos(phi)/v' = cos(phi)/sqroot(3.25 - 3*sin(phi))
theta = arcsin(cos(phi)/sqroot(3.25 - 3*sin(phi)))