Only one question per posting is allowed. Hence we are answering question no. (8)
As per the given information we consider the locations of ship-A and Ship-B at any instant t in X-Y coordinate system as shown in figure.
At any instant t, coordintates of Ship-A and ship-B are (-10t, 0), (0, 100-10t) respectively.
where t is in hours and distances are measured in km.
Distance S between Ship-A and Ship-B is given by, S2 = 100t2 + (100-10t)2 .................(1)
if we differentiate eqn.(1), 2S×(dS/dt) = 200×t + 2×(100-10×t)×(-10) = 400×t - 2000 ...............(2)
distance S is mimimum, when (dS/dt) = 0. This condotion we get in eqn.(2), when t = 5 hour