Answer to Question #101102 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

If we only think about the horizontal direction then there is no force acting in the direction

$time taken = distance/speed$

time taken = 2.2/14.6 = 0.15 seconds

displacement in the vertical (y) direction in downward direction in 0.15 seconds

= $ut + 1/2gt^2$ = 0+1/2*9.8*(0.15)2 = 0.11 m

Y= (1.8-0.11)m = 1.69 m