how to solve this battle bus physics problem?

https://isaacphysics.org/questions/battle_bus?stage=university

For part a), I don't know how you can use the cosine rule to solve this, as I can't get the velocity at r using the sine rule as it gives me a calculator error.

I thought maybe you had to use r = 1000m to calculate the speed via 1000/cos(30)x96 or 1000/sin(30)x96 but that doesn't get the answer either.

Quite confused...

Reply 1

Joinedup

I guess you're trying to incorrectly do a vector addition of the velocity of the bus to the velocity during the parachute - my understanding of the question is that the velocities are not added and that both speeds are relative to the ground.

These types of problem are often set up as swimming across rivers of negligible water velocity and then walking along the river bank in order to reach a point in the smallest possible time - they've tried to disguise it but the essentials are the same, make a trip in two straight legs at 2 different, constant speeds minimising time taken.

Have a look at the following solution to a related time optimisation problem and see if it helps
https://www.mathstat.dal.ca/rkeeping/swimproblem.pdf

also videos
https://www.youtube.com/watch?v=Z_9W0AXCElI
https://www.youtube.com/watch?v=41uyd2wcfh8

(in order to get the time you'd take the answer for x and feed it back into the first equation)