The cork from a champagne bottle slips through the hands of a waiter opening it, moving with an initial velocity v0 = 15.6 m/s at an angle θ = 77.4° 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. Part (a) Calculate the time, td in seconds, for the cork to reach the diner. Part (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.
The cork from a champagne bottle slips through the hands of a waiter opening it, moving with an initial velocity v0 = 15.6 m/s at an angle θ = 77.4° 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.
Part (a) Calculate the time, td in seconds, for the cork to reach the diner.
Part (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.
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