Question

A soccer player kicks a rock horizontally off a 39.4 m high cliffinto a pool of water. If the player hears the sound of the splash3.04 s later, what was the initial speed given to the rock? Assumethe speed of sound in air to be 343 m/s.

What I have done:

v((2 * delta y)/a) so v((2*39.4)/(9.8)) ˜ t˜2.84s

3.04 - 2.84 = 0.20s

343 * 0.20 gives me a resultant vector of 68.6m

resultant2 - delta y2 = delta x2

so 68.62 - 39.42 =delta x2

so delta x2 = 3153.6

therefore delta x = 56.156 ˜ 56.2m

delta x = initial velocity * t + (1/2)(a)(t2 )

so 56.2 = initial velocity (2.84) +(1/2)(9.8)(2.842)

when I work this out I get an initial velocity of 5.88m/s, andthe homework website says it is incorrect...where am I goingwrong?