Question

(3) Two cars collide and stay stuck together. Determine the final velocity. The first vehicle has a mass of M1 = 2Kg and moves with a speed of 30 m/s traveling in a direction 30 degrees south of east. The other vehicle has a mass of M2 = 3Kg and moves with a speed of 50 m/s in a direction 45 degrees west of north. Express the velocities as vectors and use the relevant physical principle to solve the problem. (4) Calculate the center of mass/gravity for 5 objects each of mass M1 =1 Kg, M2 = 2Kg, M3=3Kg, M4=4Kg, M5 = 5Kg. They are at the respective positions of (-3,7), (-4,-4),(5,9),(0,0),(1,17). (5) Determine the magnitude and direction of the resultant vector from adding the vectors V1, V2,V3 where V1 is a vector of length 5 in a direction 33 degrees north of east, V2 is a vector of length 10 pointed in a direction of 20 degrees west of north, and V3 is of length 20 pointed in a direction of 35 degrees south of west.

Answer 1

3)

Angular momentum is conserved in both direction

Along horizontal direction

v1 velocity of car1

v2 velocity of car2

vx final velocity

m1 x v1 x cos(30) + m2 x v2 x cos(45) = (m1 +m2) vx

Therefore

vx = 31.61 m/s

Similarly

Along vertical direction

v1 velocity of car 1

v2 velocity of car 2

vy final velocity

m1 x v1 x sin(30) + m2 x v2 xsin(45) = (m1 + m2) x vy

Therefore

vy = 27.213 m/s

Final velocity 'v'

v=vx i + vy j

=31.61 i + 27.213 j