I really need help ASAP on Physics problem 1. A 1400-kg car traveling east at 25

Question

I really need help ASAP on Physics problem

1. A 1400-kg car traveling east at 25m/s collides with a 1800-kg car traveling at a speed of 20m/s in a direction that makes angle of 40o south of west. The cars stick together after the collision. What is the magnitude and direction of the velocity of the cars after the collision?

2. A 1400-kg car traveling east at 25m/s collides with a 1800-kg car traveling at a speed of 20m/s in a direction that makes angle of 40o south of west. The cars stick together after the collision. What is the magnitude and direction of the velocity of the cars after the collision?

3. A bullet of mass m is fired at speed v0 into a wooden block of mass M. The bullet instantaneously comes to rest in the block. The block with the embedded bullet slides along a horizontal surface with a coefficient of kinetic friction u. What is the algebraic expression which determines how far the block slides before it comes to rest (the magnitude of displacement s in the figure)?

Explanation / Answer

according to conservation of linear momentum

m1*v1 + m2*v2 = (m1+m2)*v2

V2 = ((m1*v1)+(m2*v2))/(m1+m2)

m1 = 1400      v1 = 25 i m/s

m2 = 1800 kg    

v2= -20*cos40 i + 20*sin40 j

v2 = -15.32 i + 12.86 j

V = ((1400*25i) + (1800*(-15.32i + 12.56j))/(1400+1800)

V = 2.32 i + 7.065 j

magnitude V = 7.44 m/s

direction = 71.82 north of east

2) same as 1

3) m*Vo = M*V

V = m*vo/M

work energy theorem

KE = Wf

0.5*(M+m)*V^2 = u*(M+m)*g*s

s = V^2/2g = (m^2*vo^2) / (2*M^2*g)

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