Re: How far could an arrow go?
1/2 mile seems a little far. That is 880 yards. I would be surprised if it would go 440 yards. Check this formula out for how far it will go if you miss a target.
An arrow is shot from a point 20 feet above the ground with an initial horizontal Velocity of 45 feet per second and an initial vertical velocity of 80 feet per second. The parametric equations that describe the arrows path are:
x(t) =45t
y(t) = 20+80t -16squared
The arrow is aimed at a target that is horizontal distance of 90 feet from the point where the arrow is shot. If the arrow hits the target, how high is the target? If the arrow doesnt hit the target, how far does the arrow travel before it hits the ground?
Solution 28305
x(t) = 45t
y(t) = 20 + 80t – 16(t^2)
a)
Arrow hits the target:
x(t) = 90
45t = 90
45t / 45 = 90 / 45
t = 2
Find the height of the target when t = 2:
y(2)
= 20 + 80(2) – 16(2^2)
= 20 + 160 – 64
= 116
The height of the target is 116 ft.
b)
Find the time when y(t) = 0, and t > 0:
y(t) = 0
20 + 80t – 16(t^2) = 0
[20 + 80t – 16(t^2)] / 4 = 0 / 4
5 + 20t – 4(t^2) = 0
(-4)(t^2) + 20t + 5 = 0
Apply quadratic formula:
http://www.gomath.com/htdocs/lesson/quadratic_lesson3.htm
t
= {-20 – sqrt[20^2 – 4(-4)(5)]} / [2(-4)]
= {-20 – 4[sqrt(30)]} / -8
= (5/2) + (1/2)[sqrt(30)]
Find the horizontal distance traveled by the arrow:
x(5.24)
= 45(5.24)
= approximately 236
The arrow travels 236 ft before it hits the ground.