Projectiles (1 Viewer)

Sien · Mar 21, 2016

The 2 circle Qs I'm stuck on
1st I'm like stuck lol
2nd one i can't get the same answer as the book
Test tmr sos

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Drongoski · Mar 21, 2016

Is this from Cambridge (Pender et al)? If so, I've written out the solution to almost all the questions.

InteGrand · Mar 21, 2016

Sien said:
The 2 circle Qs I'm stuck on
1st I'm like stuck lol
2nd one i can't get the same answer as the book
Test tmr sos

Sent from my D6503 using Tapatalk

$\noindent The 13 (b) one is a special case of a classic physics problem known as \textit{The Monkey and the Hunter}:$

https://en.wikipedia.org/wiki/The_Monkey_and_the_Hunter

$\noindent Basically, if a hunter aims his gun so that it faces a monkey in a tree in a straight line, and fires, and the monkey drops from the tree at the instant of firing, the bullet will hit the monkey, and this happens regardless of the initial firing speed $V$ (assuming the bullet can reach the horizontal distance to the tree before hitting the ground of course). This can be proved in generality as follows:$

$\noindent The trajectory of the bullet if there were no gravity would be a straight line $y = \left(V\sin \theta \right)t$, where $\theta$ is the angle of the line connecting the hunter to the monkey in the tree with respect to the horizontal. But due to gravity, the bullet falls below the line by an amount of $\frac{1}{2}gt^2$ (in other words, the actual trajectory of the bullet is $y = \left(V\sin \theta\right) t -\frac{1}{2}gt^2$). But the distance fallen by the monkey after time $t$ is $\frac{1}{2}gt^2$ (by the standard physics formula $s = ut+\frac{1}{2}at^2$, where $u=0$ since the monkey just dropped, and $a=-g$ by gravity. Of course for HSC maths purposes, all these formulae should be derived from calculus rather than quoted like in physics).$

$\noindent So at any time $t$, the amount the bullet is below the straight line is equal to the amount the monkey has fallen from its original tree height. So at the instant the bullet has reached the horizontal distance of the tree, it is below the tree by an equal amount the monkey has fallen, meaning that it hits the monkey at this point (since they are at the same horizontal distance from the hunter at this point, and they are the same vertical distance below the tree, so they are at the same point).$

Sien · Mar 21, 2016

Drongoski said:
Is this from Cambridge (Pender et al)? If so, I've written out the solution to almost all the questions.

It's Fitzpatrick

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Projectiles (1 Viewer)

Sien

将来: NEET

Drongoski

Well-Known Member

InteGrand

Well-Known Member

Sien

将来: NEET

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