A particle falling under gravity describes 80 ft in a certain second. How long does it take to describe the next 112 ft $(g=32{\text{fts}}^{-2})$   

Initial velocity u = 0 : time t = n : Acceleration a=32ft/s2

Distance travelled in x sec Sx=80ft

Sn=u+(n−12)a⇒80=(n−12)32⇒n=52+12=3s

Final velocity after 3 seconds v=u+at

v=0+32×3=96ft s−1

Distance travelled s = 112 ft, time taken to travel t = t

s=ut+12at2

⇒112=96t+16t2⇒7=6t+t2

⇒t2+6t−7=0⇒(t−1)(t+7)=0

t = 1s.