Limo kicks a ball vertically upwards from 1m above the ground at 18m/s. It rises to its highest point and then falls down, just getting caught on a branch 5.5m above the ground. (ignore any sideways movement) How long is the ball in flight?
Tr = (Vf-Vo)/g.
Tr = (0-18) / -9.8 = 1.84 s. = Time to rise to max ht.
hmax = ho + (Vf^2-Vo^2)/2g.
hmax = 1 + (0-(18)^2) / -19.6 = 17.5 m.
above gnd.
d = Vo*t + 0.5g*t^2 = 17.5-5.5.
18t + 4.9t^2 = 12.0.
4.9t^2 + 18t - 12 = 0.
Use Quadratic Formula:
Tf = 0.576 s. = Time to fall to 5.5 m.
Tr + Tf = 1.84 + 0.576 = 2.42 s. = Time
in flight.