Question

In the figure, the LORAN stations at A and B are 700 mi apart, and the ship at P receives station A's signal 2640 microseconds (µs) before it receives the signal from station B.

(a) Assuming that radio signals travel at 980 ft/µs, find |d(P, A) − d(P, B)|.

|d(P, A) − d(P, B)| =

490 Mi <--- done

(b) Find an equation for the branch of the hyperbola indicated in red in the figure. (Use miles as the unit of distance.)


`(y^2)/(60025)-(x^2)/(62475)=1`

Done



(c) If A is due north of B, and if P is due east of A, how far is P from A? (Round your answer to one decimal place.)

I can't find the answer

Answer 1

To find the distance between P and A, we can use the equation of the hyperbola indicated in red in the figure:

(1/60025) * y^2 - (1/62475) * x^2 = 1

Since P is due east of A, the y-coordinate of P will be 0. Plugging in y = 0 into the equation, we can solve for x:

(1/60025) * (0)^2 - (1/62475) * x^2 = 1

0 - (1/62475) * x^2 = 1

Simplifying the equation:

x^2 = -62475

Since we are dealing with distances, we can ignore the negative solution. Taking the square root of both sides:

x = √62475

Calculating the value:

x ≈ 249.95

Therefore, P is approximately 249.95 miles away from A.