Heather and jerry are standing on a bridge 51 m above a river. heather throws a rock straight down with a speed of 17 m/s . jerry, at exactly the same instant of time, throws a rock straight up with the same speed. ignore air resistance.
how much time elapses between the first splash and the second splash?

Jerry throws his rock up at 20 m/s. It will decelerate at the rate of 9.8 m/s^2, until it's velocity reaches zero. At that time it will reach apogee, and begin falling. So (20 m/s)/(9.8m/s^2) =2.04 seconds To reach max height. 

After 2.04 seconds it will begin accelerating downward, again by 9.8m/s^2. So after another 2.04 seconds, it will be at the starting point, traveling at 20 m/s. It will then follow the same time path as Heather's rock. 

So Jerry's rock will take 4.08 seconds longer than Heather's to hit the water. The height above the water is not necessary information for this problem.

Hello there.

Heather and Jerry are standing on a bridge 51 m above a river. Heather throws a rock straight down with a speed of 17 m/s . Jerry, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance.
How much time elapses between the first splash and the second splash?

 4.08