A particle falling under gravity describes 80 ft in a certain second. How long does it take to describe the next 112 ft (g=32fts⁻²).   

Initial velocity, u =0; time = t; Acceleration, a=32 ft/s²

Distance travelled in x sec s_x=80ft

S_n=u+(n−$\frac{1}{2}$)a

⇒80=(n−$\frac{1}{2}$)32

⇒n=$\frac{5}{2}$+$\frac{1}{2}$=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+$\frac{1}{2}$at²

⇒112=96t+16t²⇒7=6t+t²

⇒t²+6t−7=0⇒(t−1)(t+7)=0

t = 1s