Answer the following problems based on the figure below.

Problem 1: ForΔd_y = 0 and for any given v_o find θ so that the range (Δd_x) is maximum.

Problem 2: Find the maximum height (h) and range for v_o = 10 m/s, θ = 30°, and Δd_y = -10 m. What is the flight time?

Problem 3: Find the maximum height and range for v_o = 10 m/s, θ = 30°, and Δd_y = 1 m. The displacement  Δd_y corresponds to the stage of the projectile flight where it is moving downward. What is the flight time?

Problem 4: Find Δd_y for v_o = 10 m/s, θ = 30°, and Δd_x = 15 m. What is the flight time?

Problem 5: Find the maximum height and range for v_o = 10 m/s, and θ = 90°.