A car with mass 1155 kg, moving at 32 m/s,strikes a(n) 2553 kg car at rest.If the two cars stick together, with whatspeed do they move? answer in...

In this problem the kinetic energy of the first car before striking the second car will be same as combined the kinetic energy of the two cars when they move together.

We know kinetic energy (k) of a moving object is given by the formula:

k = (mv^2)/2

Given:

Mass of car 1 = 1155 kg = m1

Velocity of car 2 = 32 m/s = vb

Mass of car 2 = 2553 kg = m2

We have to find combined velocity (va) of the to two cars after striking.

Kinetic energy of car 1 before striking (kb) is calculated from the formula of kinetic energy as:

kb = (m1*vb^2)/2 = (1155*32^2)/2 = 1155*512

Similarly kinetic energy of both cars after striking (ka) is given by:

kb = [(m1+m2)*vb^2)]/2 = [(1155+2553)*vb^2)]/2 = 1854*vb^2

We know kb = ka

Therefore: 1155*512 = 1854*vb^2

Therefore: vb^2 = (1155*512)/1854 = 17.8596 m/s

Answer:

Two cars move together with speed of 17.8596 m/s.