Final answer:
The height of the bridge from which the stone was thrown is approximately 0.625 meters, calculated using kinematic equations for projectile motion, considering the initial velocity, angle, time, and gravitational acceleration.
Step-by-step explanation:
To determine the height of the bridge from which a stone is thrown, we use the kinematic equations for projectile motion. Given that the initial velocity of the stone is 25 m/s at an angle of 30 degrees with the horizontal, we can calculate the initial vertical velocity component (Vy) using the equation:
Vy = V * sin(θ)
Where V = 25 m/s and θ = 30 degrees. Using the sine function:
Vy = 25 * sin(30) = 25 * 0.5 = 12.5 m/s
The total time t taken for the stone to hit the water is 2.5 seconds. We can use the vertical motion equation to calculate the height (h), which is:
h = Vy * t + (1/2) * g * t^2
Since the stone is thrown downwards, gravity will act to increase its velocity, therefore, we use the gravitational acceleration (g) as 9.8 m/s². Plugging in the values we get:
h = 12.5 m/s * 2.5 s + (1/2) * (-9.8 m/s²) * (2.5 s)^2
h = 31.25 m - (1/2) * 9.8 * 6.25
h = 31.25 m - 30.625 m
h = 0.625 m
Therefore, the height from which the stone was thrown is approximately 0.625 meters above the water surface.