Answer:
57.1 meters
Step-by-step explanation:
the distance the body has fallen is given by
d = 1/2 a t^2 with a = 9.8m/s^2 this becomes
d = 4.9 t^2
now we want the distance in one more second to equal the distance fallen before that one second
or 4.9 t^2 = 4.9 (t+1 )^2 - 4.9 t^2 re-arrange
2 * 4.9 t^2 = 4.9 (t+1)^2 simplify to
0 = - 4.9 t^2 + 9.8 t + 4.9 use Quadratic Formula to find
t = 2.414
then t +1 = 3.414
this corresponds to distance d = 1/2 at^2 = 1/2 ( 9.8) (3.414)^2 = 57.1 meters
check: in 2.414 seconds distance = 1/2 a t^2 = 28.6
in one second more distance = 1/2 (9.8)(3.414)^2 = 57.1
so in the last one second it has fallen approx another 28.6 m
Check !