pLEase heLp mE with thiS..,,thank yU!?

Question

A car has a mass of 1800 kg. It is traveling at a velocity of 17m/s northward. A gravel and sand delivery truck with a mass of 3000 kg moving at 20m/s southward collided head on with the car. They stick together upon colliding with each other. Find their common velocity after the collision.

please identify the given, formula and solution..,thank you..

Answer 1

Momentum conservation at frontal collision :

m = mass of the car.
M = mass of the truck.
vi = velocity of the car
Vi = velocity of the truck.
V = final velocity of (car +truck)

Northward I chose negative velocity;
Southward positive velocity. Remember that they were on opposite directions !

m vi + M Vi =(M+m) V

1800*( -17 ) + 3000 *(20) = 4800 *V

V=6.125 m/s southward , almost 6 m/s.

Answer 2

Total momentum after collision = Total momentum before collision

use the formula---(m1+m2)v=m1v1+m2v2

>>(1800+3000)v = (1800x17)+(3000x(-20))

use the calculator and find v. (-20 indicates that the truck is at the opposite direction)

Answer 3

m1u1+m2u2=v(m1+m2)

m1=1800kg
u1=17m/s
m2=3000kg
u2=-20m/s (coz in different direction)

(1800)(17)+(3000)(-20)=v(4800)
v=-6.125

negative means finally both the car n the truck move southward.

Answer 4

m1v11 + m2v21 = m1v12 + m2v22
v12 = v22 = v2
m1v11 + m2v21 = (m1 + m2)v2
v2 = (m1v11 + m2v21)/(m1 + m2)
Taking North as positive,
v2 = (1800*17 - 3000*20)/4800
v2 = (30600 - 60000)/4800
v2 = (- 29400)/4800
v2 = - 6.125 or 6.125 southward