At noon, ship a is 50 nautical miles due west of ship b. ship a is sailing west at 22 knots and ship b is sailing north at 20 knots. how fast (in knots) is the distance between the ships changing at 5 pm? (note: 1 knot is a speed of 1 nautical mile per hour.)

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

see earlier answer

the answer is false. this is because for ice to melt, it requires latent heat of melting. latent heat means heat energy required to change phase without any increase in temperatures. therefore, the ice will take energy from the environment to melt hence atmospheric temperatures will reduce.