# maths

posted by on .

a boat sails in a straight line, its position at time t is (-t+600,2t-300). a man stands on a small island, at position (200,100). due to fog, he can see objects of radius 200m centred at his position.

a) find the poitns where the line of travel of the boat intersects the circle.

b) find the duration of the period during which the man can see the boat, and the distance travelled by the boat during that time, to the nearest metre.

This is hard to explain, on a navigation plotting board, it is easy.

Here is what I recommend.

Plot the points
1) 200,100, and a 200 radius circle around that point.
2) 600, 300 (the position of the boat at time zero).

Now draw a line from the boat position at time zero with a slope of -2 (right 100, down 200). Note where it intersects the circle (two places). Between these two places is when the boat is visible.

Analytically, write the equation for the circle. Write the line equation. solve for the two points of common intersection.

solve for the time (time can be solved from either the x or y of the points, since t is in the points on the line equation..

This is hard to explain, on a navigation plotting board, it is easy.

Here is what I recommend.

Plot the points
1) 200,100, and a 200 radius circle around that point.
2) 600, 300 (the position of the boat at time zero).

Now draw a line from the boat position at time zero with a slope of -2 (right 100, down 200). Note where it intersects the circle (two places). Between these two places is when the boat is visible.

Analytically, write the equation for the circle. Write the line equation. solve for the two points of common intersection.

solve for the time (time can be solved from either the x or y of the points, since t is in the points on the line equation..