A projectile is launched on level ground at an angle theta from the horizontal with initial speed v0. It reaches the ground again at a time t and at a location x, y.

1. Discover a general expression for the time it takes to rise to the maximum height (your answer should be in terms of theta, v0, and g.

2. Discover a general expression for the maximum height relative to a coordinate system located at the initial launch point. (Your answer should be in terms of theta, v0, and g)

3. If this projectile is now launched horizontally from a rooftop, 45 meters above the ground, with an initial speed of 10 m/s, discover the projectile’s position and speed after 0.5 seconds relative to a coordinate system located at the edge of the rooftop.