Your bumper car is travelling at 2m/s. The total mass of you and your car is 350kg. a 90kg person is in your path. You crash into him and he falls into your car (so it is a perfectly inelastic collision). What is your new speed in m/s ?
We can use the conservation of momentum principle to solve this problem. Before the collision, the total momentum of the system (you and your car) is:
p1 = m1*v1 = 350 kg * 2 m/s = 700 kg*m/s
where m1 is the total mass and v1 is the initial velocity. After the collision, the person joins the system and the mass becomes:
m2 = m1 + mperson = 350 kg + 90 kg = 440 kg
The final velocity of the system can be calculated using conservation of momentum:
p1 = p2
m1*v1 = m2*v2
(350 kg * 2 m/s) = (440 kg) * v2
v2 = 1.59 m/s
Therefore, your new speed after the collision is 1.59 m/s.