Solve the all parts of given problem:
Problem: A ball is thrown with an initial speed vi at an angle (theta)sub i with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/10. In terms of R and g, find the following.
Part 1: Find the time interval during which the ball is in motion?
Part 2: Find the balls speed at the peak of its path?
Part 3: Find the initial vertical component of its velocity?
Part 4: Find its initial speed?
Part 5: Find the angle (theta) sub i?
Part 6: Suppose the ball is thrown at the same initial speed as found in part 4. But at an angle appropriate for reaching the greatest height that it can. What is maximum height?
Part 7: Suppose the ball is thrown at the same initial speed as in part 4. But at an angle for the greatest range what is the maxima range?
Please show all work and steps I am really trying to learn this for my test.