Question

A car moving with an initial speed v collides with a second stationary car that is 51.7 percent as massive. After the collision the first car moves in the same direction as before with a speed that is 35.3 percent of the original speed. Calculate the final speed of the second car. Give your answer in units of the initial speed (i.e. as a fraction of v).

Answer 1

1.25 v

Step-by-step explanation:

m₁ = mass of first car = m

m₂ = mass of the second car = (0.517) m₁ = (0.517) m

v₁ = initial velocity of first car before collision = v

v'₁ = final velocity of first car after collision = (0.353) v₁ = (0.353) v

v₂ = initial velocity of second car before collision = 0

v'₂ = final velocity of second car after collision = ?

Using conservation of momentum

m₁ v₁ + m₂ v₂ = m₁ v'₁ + m₂ v'₂

(m)(v) + ((0.517) m)(0) = (m)((0.353) v) + ((0.517) m) v'₂

v = (0.353) v + (0.517) v'₂

(0.517) v'₂ = v - (0.353) v

(0.517) v'₂ = (0.647) v

v'₂ = 1.25 v