My Math Forum Bird flying at a height $h$ above ground at constant speed of 10m/s.

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November 15th, 2015, 07:50 AM   #1
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Bird flying at a height $h$ above ground at constant speed of 10m/s.

A bird is flying in a horizontal straight line $AB$, $h$ meters above level ground. It flies over point $O$ on the ground where there is a hunter with a shotgun. The hunter fires directly at the bird when it is at $A$, where $OA$ makes an angle of $arctan(\frac{4}{3})$ with the horizontal, as shown on the enclosed diagram. $O_x$ and $O_y$ are horizontal and vertical axes respectively, and the units of $x$ and $y$ are metres. The shot leaves the gun at a speed of $80 m/s$, and air resistance on the shot is to be neglected.

The equation of the path of the shot is:

$$y=\frac{4}{3}x- 4.9(\frac{x}{48})^2$$ where

$$x = 48t$$ and
$$y= 64t - 4.9t^2$$

The bird is flying at a constant speed of $10 m/s$ and the shot hits at $B(x_1 , h)$. Show that $h = \frac{19}{18}x_1$.
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Last edited by Statistics132; November 15th, 2015 at 08:02 AM.

 February 12th, 2016, 05:09 PM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Before anyone can "Show that $h= \frac{19}{18}x_1$, we would have to know what $x_1$ is! And that is not mentioned anywhere.

 Tags $h$, 10m or s, bird, constant, flying, ground, height, speed

a bird is flying in a horizontal straight line ab, h metres above level ground

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