A child is in danger of drowning in the Merimac river The Me

A child is in danger of drowning in the Merimac river. The Merimac river has a current of 3.1 km/hr to the east. The child is 0.6 km from the shore and 2.5 km upstream from the dock. A rescue boat with speed 24.8 km/hr (with respect to the water) sets off from the dock at the optimum angle to reach the child as fast as possible. How far from the dock does the boat reach the child?

Solution

a = 0.6 km , b = 2.5 km

v = 24.8 km , u = 3.1 km

c = sqrt (a² + b²) = sqrt (0.6² + 2.5²) = 2.57 km

t = c/v = 2.57 / 24.8 = 0.104 s

d = b - ut = 2.5 - (3.1 * 0.104) = 2.18 km

distance D = sqrt(a²+ d²)

= 2.26 km