Answer
1.29 m/s.
Work Step by Step
The diver should travel 1.75 m horizontally in the time that she falls 9.00 m vertically.
Find the time to fall 9.00 m.
$y-y_o=v_{oy}t+0.5at^2$
$-9.00m= 0 + (-4.90m/s^2)t^2$
$t=\sqrt{\frac{-9.00m}{-4.90m/s^2}}=1.355 s$
Now find the velocity needed to travel 1.75 m horizontally in that time.
$v_x = \frac{1.75m}{1.355s}=1.29 m/s$
