The secret is to spread the momentum of the falling body out over a larger surface area. The trapeze artist represents a falling body with a certain amount of mass. The Earths mass exerts a force of attraction on the mass of the trapeze artist, this is known as the force of gravity. In this example, each second the artist is falling, he/she is experiencing an acceleration downward by 9.8 meters/second/second. The momentum generated by this acceleration is quite a large force by the time the artist reaches the bottom, and, if there were no net, experienced an immediate negative acceleration when he/she contacted the Earth. This force is lessened by two things: 1) the large surface area of the net, and 2) the elasticity of the net. Between those two factors, the large force is diluted by spreading it over a larger area. It is lessened further by the elasticity of the net, which absorbs some of the momentum generated by the trapeze artists body.
Impulse is defined as the product of force applied to an object times the amount of time that force is applied (F * t). The impulse applied to an object is equal to the object's change in momentum (mass times change in velocity). When a car hits a median, (heavan forbid) if there is just cement in the way then the time of impact will be extremely short. If there are crash barrells in the way then the time of impact will be many times longer (although still short) making the force many times less.
In both cases, the car is traveling a certain speed and comes to rest making the change in momentum identical in both cases. However, with the crash barrels in place let's say the time is only doubled. If so, then to keep the impulse the same as the change in momentum, the force of impact with the crash barrells would have to be cut in half.
Impulse = Change in Momentum
F * t = m v final - m v initial
That is why cushioning, air bags, bumpers crumple zones are all engineered into your vehicle. They increase the time of impact to lessen the force of impact for the rider.