To find the position of the stone after 25 seconds when the stone is dropped at a constant speed of 1 meter per second from a bridge 23 meters above the river, follow these simple steps:
1. Identify the initial conditions:
- Initial height of the stone above the river (bridge height): 23 meters
- Speed at which the stone falls: 1 meter per second
- Time the stone is falling: 25 seconds
2. Calculate the total distance the stone falls:
The stone falls at a constant speed of 1 meter per second. To find the distance the stone travels in 25 seconds, we multiply the falling speed by the time:
[tex]\[ \text{Distance fallen} = \text{Speed} \times \text{Time} \][/tex]
[tex]\[ \text{Distance fallen} = 1 \text{ m/s} \times 25 \text{ s} \][/tex]
[tex]\[ \text{Distance fallen} = 25 \text{ meters} \][/tex]
3. Find the position of the stone after 25 seconds:
The position of the stone is the initial height above the river minus the distance it has fallen:
[tex]\[ \text{Position after 25 seconds} = \text{Initial height} - \text{Distance fallen} \][/tex]
[tex]\[ \text{Position after 25 seconds} = 23 \text{ meters} - 25 \text{ meters} \][/tex]
[tex]\[ \text{Position after 25 seconds} = -2 \text{ meters} \][/tex]
4. Interpret the position:
A position of -2 meters would imply that the stone is 2 meters below the surface of the river. However, since we are only concerned with the stone's position relative to the river's surface when it hits the water, we can consider the position of the stone to be at the river's surface the moment it reaches or passes 0 meters. Thus:
At t = 25 seconds, the stone has surpassed the initial height of the bridge and has hit the river. Therefore, the position of the stone is considered to be at the river surface, which is 0 meters.
In conclusion, after 25 seconds, the stone will have hit the river, and its position relative to the river's surface is 0 meters.
