Answer: 31 m/s due east
Explanation: this question can be solved using the law of conservation of linear momentum.
This law states that in a closed or isolated system, during collision, the vector sum of momentum before collision equals the vector sum of momentum after collision.
Momentum = mass × velocity
From our question, our parameters before collision are given below as
Mass of car = mc = 1400kg
Speed of car =vc = 31 m/s (due east)
Mass of truck = mt = 2400kg
Velocity of truck = vt = 25 m/s ( due east )
After collision
Velocity of car = ?
Velocity of truck = 34 m/s ( due east )
Vector sum of momentum before collision is given as
1400 (31) + 2400 (25) = 43400 + 60000 = 103400 kgm/s
After collision the truck is seen to move faster (v = 34 m/s) which implies that the car also moves due east .
1400 (v) + 2400(25) .... A positive value is between both momenta because they are in the same direction.
After collision, we have that
1400v + 60000
Vector sum of momentum before collision = vector sum of momentum after collision
103400 = 1400v + 60000
103400 - 60000 = 1400v
43400 = 1400v
v = 43400/ 1400
v = 31 m/s due east
