Could someone please help me with this question
View attachment 36654
Just a rough outline;
equation of motion for hunters arrow is:
x = vtcos(A), y = vtsin(A) - gt^2/2
equation of motion for monkey is:
y = h-gt^2/2 and x = d
As noted and from the diagram, the initial velocity is such that it can reach the tree and so the angle of launch must be:
tanA = h/d
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Suppose for contradiction that the hunter's arrow never hits the monkey so:
y_1 = y_2:
vtsinA - gt^2/2 = h -gt^2/2
vtsinA =h
x_2 = x_1:
vtcosA = d
So these two equations above are false i.e vtsinA =/ h and vtcosA =/ d on the basis of our assumption.
However using these equations:
vtsinA/vtcosA =/ h/d
tanA =/ h/d
So tanA =/ h/d but we already know that tanA = h/d so there's a contradiction. Hence our original assumption must be false and so regardless of V, the hunter's arrow must hit the monkey
