Find the optimal time τ for foraging in the Wadden Sea, such that the red knot will arrive inSouth Africa at the earliest possible moment. At what speed would the red knot fly? Whatwould be the travelling time in that case? And what would be the total time after which thered knot arrives

As a crude approximation, we assume that the (constant) speed at which the birds make theirjourney increases linearly with the time they spend foraging for energy before commencing it,through the following formula:v0 = 50 + 3 τ, (8)where τ is the time in days that the red knot spends foraging in the Dutch Wadden Sea and v0 isthe constant speed in km per day at which it will be able to travel the entire journey of 9000 km.(b). Explain that the total time before the red knot arrives in South Africa will be given byT = 900050 + 3 τ + τ.

o it makes sense to generalize this model to anydistance d and the (constant) migration speed v0, still assuming it will depend linearly on the timespend foraging before taking off, would be given byv0 = a + b τ, (10)where τ is the time in days that the red knot spends foraging in the Dutch Wadden Sea and v0 isthe constant speed in km per day at which it will be able to travel the entire distance d and thecoefficients a and b are constants that may be different for different species of migrating birds.(d). Show that the total time before the bird arrives at their wintering grounds would be given byT = da + b τ + τ.

The knot is a unit of speed equal to 1.852 km/hour.A boat travels 100 metres in 7 seconds. How many knots is this?Give your answer to two significant figures.

Find the optimal time τ for foraging in preparation for the journey, expressed in terms of theparameters a, b and d

oger and Caine are in a foot race. Roger is 200m ahead of Caine. However, Caine is unning10m/s while Roger is only unning at 8m/s. After what length of time would Caine take to be100m ahead of Roger?