please explain the reasoning behind the answer and any assumptions. also please

Question

please explain the reasoning behind the answer and any assumptions. also please show step by step on calculation

EXTRA CREDIT 2:20 points Tarzan is hungry and notices a bunch of banamas hanging from a tree (se figure below) He decides to throw a spear to bunch of bananas a distance h vertically above the spear and a distance R horizontally away from the spear. He aims as shown, towards tho directly at the bananas and throws the spear, but just as he throws, a banana, from the bunch, drops from the tree Answer the question "Does the spear hit the banana?" by SHOWING ALL the appropriate kinematic eauations that apply to this scenario and SOLVING them to find the final answer (I

Explanation / Answer

let assume the bananna falls height dy in time t while the spear covers the range R
hence
dy = 0.5gt^2 .. (1)

now, y coordinate of the spear in this time = vsin(theta)*t - 0.5gt^2
also, vcos(theta)*t = R
hence
y = vsin(theta)*R/vcos(theta) - 0.5gt^2 = Rtan(theta) - 0.5gt^2

also,
for the spear to hit the banana, y + dy = H
Rtan(theta) - 0.5gt^2 + 0.5gt^2 = H
but given
tan(theta) = H/R
hence
the spear will hit the banana

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