Final answer:
The stone takes approximately 3.26 seconds to fall to the water and strikes the water with a speed of about 31.95 m/s. This uses the equations of motion under constant acceleration due to gravity, ignoring the stone's initial horizontal velocity.
Step-by-step explanation:
To find out how long the stone takes to reach the water, we need to calculate the time of flight for an object in free fall that has been given an initial horizontal velocity. Here we can ignore the stone's horizontal speed since it does not affect the time taken to hit the water. We'll apply the equation of motion under constant acceleration due to gravity to calculate the time of fall.
The equation of motion we'll use is s = ut + 1/2at², where s is the displacement (52 m), u is the initial vertical velocity (0 m/s, since the stone is kicked horizontally), a is the acceleration due to gravity (9.8 m/s²), and t is the time in seconds.
Plugging the values into the equation and solving for t, we get:
- s = 1/2at²
- 52 = 1/2(9.8)t²
- 52 = 4.9t²
- t² = 52 / 4.9
- t² = 10.61224
- t = √10.61224 ≈ 3.26 seconds (Time taken for the stone to fall to the water)
To find the speed at which the stone strikes the water, we use the second equation of motion, v = u + at, where v is the final velocity.
v = 0 + (9.8 m/s²)(3.26 seconds)
v ≈ 31.95 m/s (Speed at which the stone strikes the water)