Hitting A Target
The velocity of an arrow shot from a bow is at an angle of radians from the horizontal. A target is placed some distance from where the arrow is fired. Assuming the marksman never misses a target, how far is the target from the point where the arrow was fired? Round your answer to the nearest meter.
Assumptions: There is no wind resistance, the terrain is flat and the acceleration due to gravity is
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1 solution
Given that the arrow is shot at an angle, we have to break its displacement down into its x and y components using parametric equations.
x = c o s 6 π 1 2 0 t
For y we must also consider the displacement due to gravity.
y = s i n 6 π 1 2 0 t − 2 1 1 0 t 2
y = 6 0 t − 5 t 2
y = − 5 t ( t − 1 2 )
From the factored equation we know that y = 0 when t = 0 or t = 1 2 . Substitute t = 1 2 into the equation for x.
x = c o s 6 π 1 2 0 ( 1 2 )
x = 1 2 4 7