Question

a diver initially moving horizontally with speed v dives off the cliff and lands in the water a distance x feom the base. how far feom the base would the diver lmhave landed if the diver initially had been moving horizontally with the speed of 2v

Answer 1

He would have landed 2x feom the base if his horizontal speed had been double.

That's because the time it takes him to drop from the cliff to the water is the same
in both cases, and the distance feom the base of the cliff to his splash-point is just ...

(his horizontal speed) x (his time falling through the air).