One boy standing on a bridge throws a stone horizontally at a velocity of 12m/s. If the bridge is 10m above the river, how far horizontally will the stone go from him?
how long does it take to fall 10m? 4.9t^2 = 10
Then the horizontal distance is 12t
To find the horizontal distance the stone will travel, we need to consider the horizontal component of the stone's motion. Since the stone is thrown horizontally, it will not have any vertical acceleration.
We can use the equation for horizontal distance:
distance = velocity × time
In this case, the velocity of the stone is 12 m/s, and we need to find the time it takes for the stone to reach the river.
To find the time, we can use the equation for vertical motion:
vertical distance = initial velocity × time + (1/2) × acceleration × time²
Since the stone is thrown horizontally, the initial vertical velocity is 0 m/s. The acceleration due to gravity is -9.8 m/s² (negative because it acts downwards). The vertical distance is the height of the bridge, which is given as 10 m. Solving the equation for time:
10 m = 0 × t + (1/2) × (-9.8 m/s²) × t²
10 m = -4.9 m/s² × t²
2t² = -10 m / -4.9 m/s²
t² = 2.041 s²
t ≈ √2.041 ≈ 1.429 s
Now that we have the time it takes for the stone to reach the river, we can find the horizontal distance using the equation:
distance = velocity × time
distance = 12 m/s × 1.429 s
distance ≈ 17.148 m
Therefore, the stone will travel approximately 17.148 meters horizontally from the boy.