Trig & velocity

lenisaks

New member
Joined
May 31, 2005
Messages
1
im having a hard time with this one...

"On a wall, a spider is 100 cm above a fly. The fly starts moving horizontally at the speed of 10 cm/s. After 1 second the spider begins moving at twice the speed of teh fly, in such a way as to intercept the fly by taking a straight line path. In what direction does the spider move, and how far has the fly moved when they meet?
 
If you draw it with the fly at P(0,0) and the spider at P(0,100) the fly will be at P(0,10t)
The spider will travel the hypot of a right triangle = 20(t-1) so
100²+(10t)² = (20(t-1))²
when they meet.
Solve for the time that they meet, which will give the triangle.
 
Hello, lenisaks!

On a wall, a spider is 100 cm above a fly.
The fly starts moving horizontally at the speed of 10 cm/s.
After 1 second the spider begins moving at twice the speed of the fly,
in such a way as to intercept the fly by taking a straight line path.
In what direction does the spider move, and how far has the fly moved when they meet?
Code:
     A  10   B      10t      C
     *-------+---------------*    The fly starts at A.
     |                   *        The spider is at S.
     |               *
 100 |           * 20t            One second later,
     |       *                    the fly is at B
     |   *                        and the chase begins.
     *
     S
In the next t seconds, the fly moves 10t cm to C.
In the same t seconds, the spider moves 20t cm to C.

Using Pythagorus, we have: . 100<sup>2</sup> + (10t + 10)<sup>2</sup> . = . (20t)<sup>2</sup>

. . . which simplifies to: . 3t<sup>2</sup> - 2t - 101 .= .0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .__
From the Quadratic Formula: . t .= .(1 + 4√19) / 3 . .6.145 seconds


Hence, the fly has moved: .(10)(6.145) = 61.45 cm from B to C
. . . or a total of: .10 + 61.45 .= .71.45 cm from A to C.

. . . . . . . . . . . . . . . . . . . . . . . . . .AC . . . 71.452
In right triangle SAC: . tan S .= .---- .= .--------- .= .0.71452
. . . . . . . . . . . . . . . . . . . . . . . . . .AS . . . . 100
. . . then: . S . .35.55<sup>o</sup>

[I hope the spider brought his calculator.]
 
Top