A railroad car moving at a speed of 3.49 m/s overtakes, collides, and couples with two coupled railroad cars moving in the same direction at 1.28 m/s. All cars have a mass of mass 1.08 105 kg. Determine the following.

(a) speed of the three coupled cars after the collision (Give your answer to at least 2 decimal places.)(b) kinetic energy lost in the collision

Explanation:

Using conservation law of momentum

let m₁ = mass of the railroad, initial u₁ = 3.49 m/s

let m₂ = mass of one of the coupled car,  u₂= 1.28m/s

let m₃ = mass of the second car u₃ = 1.28 m/s

m₁u₁ + m₂u₂ + m₃u₃ = v ( m₁ + m₂ + m₃)

since the masses are the same

m₁ = m₂ = m₃

m ( 3.49 + 1.28 + 1.28) = 3m v

6.05 m = 3 mv

v = 6.05 m / 3m = 2.0167 m/s

b) kinetic energy lost = energy before collision - energy after collision

= (0.5m₁u₁² + 0.5 ( m₁+m₂) u₂² - 0.5 ( m₁ + m₂ + m₃) v

= (6.58365 + 1.7712) - 6.5951 = 1.76J  

d

explanation:

v=uf/(u-f)

= 5.10/(5-10) convex lens has positive focal length

=50/-5

=-10 cm (formed at other side)

no. dot product   =0 when vecs at right angles