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Question 16 Cambridge ext 2 6F (1 Viewer)
- Thread starter Daq
- Start date
ivanradoszyce
Member
- Joined
- Oct 18, 2023
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- HSC
- 2018
Consider the diagram below.
Now consider the right angle triangle
. Using Pythagoras
^2 = (PN)^2 + (ON)^2)
To cover the entire garden bed we need to be able to reach the corner of the garden bed
. This means the distance needs to be greater or equal to 
^2 = (PN)^2 + (ON)^2
)
Since
^2 = \bigg(\frac{v^2}{g}\bigg)^2
)
Therefore
^2 = 9 + (ON)^2
)
So
^2 = \bigg(\frac{v^2}{g}\bigg)^2 - 9
)
But to cover the distance, (or in our case shown in the diagram )  + 3)
.
 + 3
)
^2 \ge \bigg[\bigg(\frac{v^2}{2g}\bigg) + 3\bigg]^2 \text{\,\,\,\,\,square both sides}
)
However, from Pythagoras.
Thus
^2 - 9 \ge \bigg[\bigg(\frac{v^2}{2g}\bigg) + 3\bigg]^2
)
Expanding and simplifying
^2 \ge 7
)
Now consider the right angle triangle
To cover the entire garden bed we need to be able to reach the corner of the garden bed
Since
Therefore
So
But to cover the distance
However, from Pythagoras.
Thus
Expanding and simplifying