Answer:
distance between the ships changing 29.255 knot
Explanation:
Given data
time = noon to 5 pm = 5 hours
A = 50 nautical miles due west of B
A = sailing west at 22 knots
B = sailing north at 20 knots
to find out
How fast is the distance between the ships changing
solution
we consider a to b distance is z and at noon ship at 90 degree angle of AB at x and y distance from AB respectively
so here z² = x² + y² ..............1
and 2z z' = 2x x' + 2y y'
so z' = ( x x' + y y' ) / z
and after 5 hours
x = 50 + 22(t) = 50 + 22(5) = 160
y = 20(t) = 20 (5) = 100
so from equation 1
z² = x² + y²
z² = 160² + 100²
z =
z = 188.68
so z' = ( x x' + y y' ) / z
z' = ( 160 (22) + 100(20) ) / 188.68
z' = 29.255
distance between the ships changing 29.255 knot
Answer: Answer Below
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