In the opening ceremonies for the 1992 Summer Olympics in Barcelona, the Olympic Torch was lit by firing a flaming arrow into the open top of the torch. Assume that the torch is of height H and that its top has a width of H/2, and that the arrow was launched at a 45° angle at a horizontal distance of 3H from the near end of the torch as shown. Air resistance can be neglected.
Potentially useful information: sin 45º = cos 45º = 1/√2 , tan 45º = 1.
a. Find the minimum launch speed of the arrow that will allow it to go into the open top of the torch. For full credit, show your work, simplify your answer, and express your answer in terms of H and g. Do not insert a numerical value of g — if you do, you will receive zero points for this part.
