Hi there!
We can use the following kinematic equation:
[tex]v_f^2 = v_i^2 + 2ad[/tex]
vf = final velocity (0 m/s at the top of the trajectory)
vi = initial velocity (at which it was thrown, ? m/s)
a = acceleration (due to gravity, 9.8 m/s²)
d = displacement of the javelin (100 m)
We can plug in the givens:
[tex]0 = v_i^2 + 2(-9.8)(100)\\\\2(9.8)(100) = v_i^2[/tex]
Take the square root to solve:
[tex]v_i = \sqrt{2(9.8)(100)} = \boxed{44.27 \frac{m}{s}}[/tex]
