Refer to the diagram shown below.
Note that air resistance is ignored, and the acceleration due to gravity is 9.8 m/s².
The vertical flight from A to B (the maximum height) and from B to C take equal amounts of time because the flight is parabolic.
The time of flight from A to C is given as 5 s, therefore the flight from A to B is 2.5 s.
Let u = vertical launch velocity (m/s).
Because the vertical velocity at B is zero, therefore
u - (9.8 m/s²)*(2.5 s) = 0
u = 24.5 m/s
Let v = the velocity with which the stone strikes the water.
The water surface is at a height of h = -25 m.
The equation governing the flight from A to the surface of the water is
v² = u² - 2gh
v² = (24.5 m/s)² - 2*(9.8 m/s²)*(-25 m)
= 1090.25
v = 33.02 m/s
Answer:
The velocity with which the stone strikes the water surface is 33.0 m/s (nearest tenth)
