First we gotta use an equation of motion:
[tex]d = ut + \frac{1}{2} a {t}^{2} [/tex]
Our vertical distance d= 100 m, initial vertical speed u = 0 m/s (because velocity is fully horizontal), and vertical acceleration a = 9.8 m/s2 because of gravity. Let's plug it all in!
[tex]100 = 0 + \frac{1}{2} (9.8) {t}^{2} [/tex]
Now we just need to solve for t:
[tex] {t}^{2} = \frac{2(100)}{9.8} \\ \\ t = \sqrt{\frac{2(100)}{9.8}} [/tex]
Hit the calculators, and you'll get 4.5 seconds!
