Projectiles question (1 Viewer)

[Chang]

A gunner needs to hit at a target 100m, 1.5m above the ground. Calculate the angle the gun needs to be held at if the muzzle velocity is 170m/s

Thx

 

[ezzy85]

derive the equations of motion from y^.. = -g and x^.. = 0


then youll get x=170cos@ t and y = -gt²/2 + 170sin@ t

make t the subject in the x equation and sub that into the y equation. youll get a cartesion equation without the t. sub in x = 100, y = 1.5 and solve for @.
for this im assuming its fired from the origin.

 

[PoLaRbEaR]

*using g=10m/s and v=170m/s derive:
y=-x(1+tan)/5780 + xtan

*sub y=1.5 and x=100
1.5 = -10000(1+tan)/5780 + 100tan
simplify and rearrange:
433.5 = -500(1+tan) +28900tan
500tan - 28900tan + 933.5 = 0

*let u = tan
500u - 28900u +933.5 = 0
u = tan = [28900 28867.68089]/1000
tan = 57.76768089 or 0.032319109


= 89 or 1 51'