Final answer:
To calculate the time it takes for a stone thrown horizontally from a bridge to strike the water 80 m below, we use the kinematic equation for vertical motion under gravity, which gives a time of approximately 4.04 seconds.
Step-by-step explanation:
To determine how long it takes for the stone to strike the water 80 m below the bridge when thrown horizontally with an initial speed of 10 m/s, we need to apply the principles of projectile motion. Since the stone is thrown horizontally, the initial vertical velocity is 0 m/s, and the horizontal velocity remains constant as we ignore air resistance. The only force acting on the stone in the vertical direction is gravity, which accelerates the stone at 9.8 m/s2 (acceleration due to gravity).
To find the time taken (t) for the stone to fall 80 m, we use the kinematic equation for vertical motion:
h = 1/2 × g × t^2
where:
- h is the height (80 m)
- g is the acceleration due to gravity (9.8 m/s^2)
- t is the time in seconds
Rearranging the equation to solve for time, we get:
t = √(2 × h / g)
Substituting the values:
t = √(2 × 80 m / 9.8 m/s^2) = √(160 / 9.8) = √(16.327) ≈ 4.04 seconds
Therefore, it would take approximately 4.04 seconds for the stone to hit the water.