Těleso urazilo za poslední dvě sekundy volného pádu třetinu svojí celko vé dráhy. Jak dlouho a z jaké výšky padalo?

s=s1+s2

t=t1+t2

s1=2/3*s; t1=? sec
s2=1/3*s; t2=2 sec
s=?
t=?

g=9,81 m/s2 (g=10 m/s2)

t2=2 sec

v1=g*t1
v2=g*t2 + v1

s1=1/2*g*(t1)² + 0
s2=1/2*g*(t2)² + v1*t2

2/3*s=1/2*g*(t1)² + 0
1/3*s=1/2*g*(t2)² + g*t1*t2

s=3/4*g*(t1)² + 0
s=3/2*g*(t2)² + 3*g*t1*t2

s=s

0 = (t1)² - 8*t1 - 8

t1=(8+√(64+4*8))/2=4+2√6

t1=4 + 2√6 = 8,8989794855663561963945681494118 sec
t2=2sec

s=3/4*9,81*(t1)² = 3/4*9,81*(8*t1 + 8) = 6*9,81*(t1 + 1) = 6*9,81*(8,8989794855663561963945681494118 + 1) = 582,65393252043572571978428127433

s=582,65 m
==========

t=t1+t2=8,8989794855663561963945681494118 sec + 2 sec

t=10,9 sec
==========

kontrola:

2/3*s=1/2*g*(t1)²
2/3*s=1/2*g*(8t1 + 8)
s=6*g*(t1 + 1)
s=6*g*((4+2√6) + 1)
s=6*9,81*((4+2*6i@) + 1)=582,65393252043572571978428127438 OK

1/3*s=1/2*g*(t2)² + g*t1*t2
s=3/2*g*(t2)² + 3*g*t1*t2
s=3/2*g*2² + 3*g*t1*2
s=6*g + 6*g*t1
s=6*g + 6*g*(4+2√6)
s=6*g*(5 + 2√6)=6*9,81*(5 + 2*6i@)=582,65393252043572571978428127438 OK