You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground. Unfortunately the archer stands on an elevated platform of unknown height. However, you find the arrow stuck in the ground 56.0 m away, making a 2.00 ∘ angle with the ground. How fast was the arrow shot?

The cork from a champagne bottle slips through the hands of a waiter opening it, moving with an initial velocity v0 = 15.5 m/s at an angle θ = 75.8° above horizontal. A diner is sitting a horizontal distance d away when this happens. Assume the cork leaves the waiter’s hands at the same vertical level as the diner and that the cork falls back to this vertical level when it reaches the diner. Use a Cartesian coordinate system with the origin at the cork's initial position. a.) Calculate the time, td in seconds, for the cork to reach the diner.  b.)  Reacting quickly to avoid being struck, the diner moves 2.00 m horizontally directly toward the waiter opening the champagne bottle. Determine the horizontal distance, d in meters, between the waiter and the diner at the time the cork reaches where the diner had previously been sitting.  Please explain how you got your answer in detail

A basketball player who is 2.00 m tall is standing on the floor 10.0 m from the basket as in figure. If he shoots the ball at a 40.0° angle with the horizontal at what initial speed must he throw so that it goes through the hoop without striking the backboard? the basket height is 3.05 m.

A student standing on a cliff throws a rock from a vertical height of d=8.0m above the level ground with velocity v0=19m/s at an angle θ=29∘ below the horizontal, as shown. It moves without air resistance. Use a Cartesian coordinate system with the origin at the initial position of the rock.  Part (a)  With what speed, in meters per second, does the stone strike the ground? Part (b)  If the rock had been thrown from the clifftop with the same initial speed and the same angle, but above the horizontal, would its impact velocity be different?