Answer:
The text you selected describes a projectile motion problem. A ball is fired at an angle of 22.5° and unknown speed. It travels a range of 30 m. The question asks for the initial velocity (magnitude and direction) of the ball, the maximum height of the trajectory, and the other angle that would give the same range with the same initial speed.
To solve this problem, we can use the following equations:
- Range = (Initial velocity)^2 * sin(2*angle) / g
- Maximum height = (Initial velocity)^2 * sin^2(angle) / 2g
- Initial velocity = Range * g / (sin(2*angle))
where g is the acceleration due to gravity.
Using these equations, we can find that:
- The initial velocity of the ball is approximately 23.6 m/s at an angle of 22.5°.
- The maximum height of the trajectory is approximately 3.8 m.
- The other angle that would give the same range with the same initial speed is approximately 67.5°.