Guide To Archery

5 Arrow

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An archer standing on a 13.2 degree slope shoots an arrow 21.5 degrees above the horizontal.?

How far down the slope does the arrow hit if it is shot with a speed of 48.8m/s from 1.85m above the ground?

There is a relationship between x and the additional fall of y
y/x=tan(13.2)

y(t)=1.85+x*tan(13.2)+
48.8*sin(21.5)*t-.5*g*t^2

when y=0, the arrow hits downslope

and
x(t)=48.8*cos(21.5)*t
plug y(t)=0 and x(t) into the y(t) equation

0=1.85+(cos(21.5)*tan(13.2)+
sin(21.5))*48.8*t-.5*g*t^2

t=5.8816 seconds
x=267.05 m this is the horizontal distance

The fall down slope vertically is
x*tan(13.2)
62.6 m

and the run is
x/cos(13.2)
274.3 m
======================

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An archer standing on a 13.2 degree slope shoots an arrow 21.5 degrees above the horizontal.?

How far down the slope does the arrow hit if it is shot with a speed of 48.8m/s from 1.85m above the ground?

There is a relationship between x and the additional fall of y
y/x=tan(13.2)

y(t)=1.85+x*tan(13.2)+
48.8*sin(21.5)*t-.5*g*t^2

when y=0, the arrow hits downslope

and
x(t)=48.8*cos(21.5)*t
plug y(t)=0 and x(t) into the y(t) equation

0=1.85+(cos(21.5)*tan(13.2)+
sin(21.5))*48.8*t-.5*g*t^2

t=5.8816 seconds
x=267.05 m this is the horizontal distance

The fall down slope vertically is
x*tan(13.2)
62.6 m

and the run is
x/cos(13.2)
274.3 m
======================

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