3) This could vary from one person to the next, but since we are making an assumption, we can say any number thats reasonably within range. So, assuming an average person is 1.76 meters tall, then while sitting on a bicycle, he should be about 1-1.2 meters tall. Let us use 1.1 meters tall whiling sitting on a bicycle.
4) Using out formula, to find the time:
Let d(t) = 1.1 meters. Hence, 1.1 m = 4.9t^2 = > (1.1/4.9)^0.5 = t .... so t = 0.4738 seconds.
5) We are given the equation: V(t) = V(0) + at , where V(t) is the velocity at some time t, V(0) is some constant (initial velocity) and a and t are acceleration and time, respectively.
Hence, plugging in 9.8 for a and V(0)=0, we get:
v(t) = 9.8t
6) Hence the velocity with which his head hits the ground is: v(0.4738 sec) = 9.8(0.4738) = 4.643 m/s
7) Our value of 4.643 is no where close to what the believed value of lasting damage is. There is a 340% error and therefore it is very unlikely that the person riding the bike will have any lasting damage. Notice however, that our result would have differed if we chose the height to be a different number. Still, I would recommend to wear a helmet because there are many factors that are not taking into consideration. For example, the speed would differ if the persons initial velocity was not zero.
Hope this helped.