Answer to Question #101097 in Classical Mechanics for Sam

Question

An arrow was shot at a target X=2.2m away. The speed of the arrow was 14.6m/s. Using g=9.8m s-2, and if the arrow was fired at a height of H=1.8m, what height above the ground (Y) does the bullseye need to ensure it is struck by the arrow (0.1m)?

See diagram below:
https://cdn.discordapp.com/attachments/523069000775761934/663875634237538336/Projectile_-_Horizontal_wall_1.PNG

Answer 1

Let the time taken by the arrow to cover 2.2 m horizontal distance $=v\times t$

$\Rightarrow 2.2 = 14.6\times t$

$\Rightarrow t=\dfrac{2.2}{14.6}=0.15sec$

In the same duration of time, arrow will cover a vertical distance of $y=ut+\dfrac{gt^2}{2}$

$\Rightarrow y=0+\dfrac{9.8\times 0.15\times 0.15}{2}=0.11m$

Hence the height of the target from the ground will be $1.8-0.11=1.69m$