A ball is thrown at 30 m/s horizontally off a building. it lands 100 meters from the base of the building. How high is the building?
To find the height of the building, we need to calculate how long it takes for the ball to reach the ground.
We can use the formula for horizontal distance to find the time of flight:
Distance = Velocity × Time
Since the horizontal velocity is constant at 30 m/s and the horizontal distance is 100 meters, we can rearrange the formula as:
Time = Distance / Velocity
Time = 100 m / 30 m/s
Time ≈ 3.33 seconds
Now that we know the time it takes for the ball to reach the ground, we can calculate the height of the building using the equation for vertical motion.
The equation for vertical distance is given by:
Distance = Initial Velocity × Time + (1/2) × Acceleration × Time^2
In this case, the initial vertical velocity is 0 m/s since the ball is thrown horizontally. The acceleration due to gravity is approximately 9.8 m/s^2. Thus, the equation becomes:
Distance = (1/2) × 9.8 m/s^2 × Time^2
Substituting the calculated time of 3.33 seconds, we can solve for the distance:
Distance = (1/2) × 9.8 m/s^2 × (3.33 s)^2
Distance ≈ 54.66 meters
Therefore, the height of the building is approximately 54.66 meters.