A stone is thrown horizontally from the top of a building with a speed of 29.5 m/sec. It lands 56.3 meters from the base of the building. How long was it in the air, and how tall is the building?
time in air (t) ... 56.3 m / 29.5 m/s
height of bldng ... 1/2 g t^2
To determine how long the stone was in the air, we can use the horizontal motion of the stone. Since it is thrown horizontally, there is no acceleration in the x-direction. Thus, we can use the formula:
Distance = Speed * Time
In this case, the distance is given as 56.3 meters, and the speed is given as 29.5 m/s. Let's rearrange the formula to solve for time:
Time = Distance / Speed
Time = 56.3 m / 29.5 m/s
Time = 1.91 seconds (rounded to two decimal places)
So, the stone was in the air for approximately 1.91 seconds.
To find the height of the building, we need to use the vertical motion of the stone. In this case, the stone is thrown horizontally, so the initial vertical velocity is zero. The only force acting on the stone is gravity, causing it to accelerate downwards at 9.8 m/s².
We can use the formula for vertical displacement to calculate the height of the building:
Vertical Displacement = (Initial Velocity * Time) + (0.5 * Acceleration * Time²)
Since the initial vertical velocity is zero, the formula simplifies to:
Vertical Displacement = 0.5 * Acceleration * Time²
The displacement is given as the height of the building, and Time is the value we calculated earlier. So, let's calculate the height:
Vertical Displacement = 0.5 * 9.8 m/s² * (1.91 s)²
Vertical Displacement = 18.78 meters (rounded to two decimal places)
Therefore, the height of the building is approximately 18.78 meters.