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Complete question:
Vector Functions and Parametric Equations
A bow-and-arrow hunter walks toward the origin along the positive x-axis, with unit speed; at time 0 he is at x = 10. His arrow (of unit length) is aimed always toward a rabbit hopping with constant velocity √5 in the first quadrant along the line y = 2x; at time 0 it is at the origin.
a) Write down the vector function A(t) for the arrow at time t.
b) The hunter shoots (and misses) when closest to the rabbit; when is that?
Answer:
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First you have to figure out what the equation of the line is. Let's use the slope formula to find the slope, and then one of the points to find the y-intercept. We'll put the line's equation in y=mx+b form.
Now, we'll use that slope in y=mx+b form with one of the coordinates in order to find what b (which is also the y-intercept) equals
therefore your y-intercept is equal to 1.5. In order to find the x-intercept we'll take our new equation
and make y = 0, because the line intersects with the x-axis when y is equal to zero.
therefore, your x-intercept is 3 and your y-intercept is 1.5
Now, we'll use that slope in y=mx+b form with one of the coordinates in order to find what b (which is also the y-intercept) equals
therefore your y-intercept is equal to 1.5. In order to find the x-intercept we'll take our new equation
therefore, your x-intercept is 3 and your y-intercept is 1.5