• • A ship travels at a constant speed of 25 kilometres per hour (Kph) in a straight line from port A located at position (x_A, y_A) =(-100, -100) to port B at (x_B ,y_B )=(300 ,100).

A) Find parametric equation for the line of travel of the ship .your equation should be in terms a parameter t, and should be such that the ship is at port A when t=0 and at port B when t=1.

(b) During its journey ,the ship passes two lighthouses ,L_1 and L_2, which are located at positions (0,0) and (200.0), respectively.

(i) write down expressions ,in terms of the parameter t of part (a) ,for the squares d_1^2 and d_2^2 of distances between the location of the ship at parameter value t and the lighthouses L_1 and L_2 respectively .Simplify your results.

(ii) Completing the square for your result for d_1^2:

d_1^2=200000((t- 3/10)^2 + 1/100)

Explain how d_1 varies as t increases from 0 to 1 .Determine the shortest distance between the ship and the lighthouse L_1, to the nearest kilometre .

(iii) Complete the square for your result for d_2^2 from part (b)(i) ,and determine the shortest distance between the ship and the lighthouse L_2 ,to the nearest kilometre.

(iv) lighthouse L1 can be seen from a distance of 50 kilometres.

Calculate the parameter values t_1 and t_2 when the lighthouse L_1 can first and last be seen from the ship. For how many minutes is the lighthouse visible from the ship?

please need your help

thanks for reading

# 5 Answers

Just take each instruction, one at a time. Don't get overwhelmed. This question is not that difficult, but seems so because there are so many steps. But if you follow the instructions, one at a time, it will be a piece of cake. This is exactly what I do whenever I fly cross country in my airplane. The only difference is instead of lighthouses, I'm using VOR's. But here is the key, find the overall distance and figure out how far you will travel per unit of time. Then plot in the lighthouses at the appropriate intervals and figure each segment of the trip by itself and compare that to the overall distance as a double check. As you work your way through the problem, think to yourself, what if I was actually in the boat or plane or whatever. When would I find the lighthouse? You could do this the way I do, by figuring each segment and then using a compass to plot the distance from each lighthouse in a circle, and then draw a straight line across the circles and then using the compass again to finger the distance through the arc of the circles. As I said, you could do it the way I would do it using a map, but you can do it via basic geometry too, which is how your teacher wants.

12 years ago. Rating: 0 | |