On August 12, 1987, Alessandro Andrei set a world record in the shot put with a throw of 22.9m. What was the initial speed of the shot if he released it at a height of 2.10m and threw it at an angle of 38 degrees above the horizontal?
To find the initial speed of the shot, we can use the principles of projectile motion. We will break down the motion into the horizontal and vertical components.
1. Determine the horizontal component of the initial velocity:
The horizontal component remains constant throughout the motion. We can use the equation:
Horizontal distance = Horizontal component of initial velocity × Time
In this case, the horizontal distance is the projection range, which is not given. However, we can assume it to be the world record of 22.9m.
Time can be found using the vertical component of the motion:
Time = Square root of ((2 × vertical distance) ÷ (acceleration due to gravity))
The vertical distance is the difference between the release height and the maximum height. In this case, it is 2.10m.
The acceleration due to gravity can be assumed to be 9.8 m/s^2.
2. Determine the vertical component of the initial velocity:
The vertical component changes due to gravity. We can use the equation:
Maximum height = (Vertical component of initial velocity)^2 ÷ (2 × acceleration due to gravity × cos^2(θ))
In this case, the maximum height is not given, but we can assume it to be equal to the release height, which is 2.10m.
θ is the angle of projection, which is 38 degrees.
3. Calculate the initial velocity:
Once we have the horizontal and vertical components of the initial velocity, we can calculate the magnitude of the initial velocity using the Pythagorean theorem:
Initial velocity = Square root of ((Horizontal component of initial velocity)^2 + (Vertical component of initial velocity)^2)
By following these steps, you can obtain the initial speed of the shot thrown by Alessandro Andrei on August 12, 1987.