Finding time from a velocity vector

[ericcy]

Homework Statement

A jet-ski driver wants to head to an island in the St.Lawrence River that is 5.0km [W20.0S] away. If he is traveling at a speed of 40.0km/h relative to the water and the St.Lawrence is flowing 6.0km/h [E], how long will it take him to reach the island?

Relevant Equations

v=d/t

I've looked it up online and someone did t=40−65=0.15(h)

I was just wondering why they would subtract the velocities. Could something explain this to me please? thanks.

 

[kuruman]

Presumably 5.0km [W20.0S] away means 5.0 km away in the direction 20 degrees West of South. Is this correct?

I've looked it up online and someone did t=40−65=0.15(h)

That's not very helpful, there are no numbers like 40 or 65 in this problem, so I cannot explain what "they" did and why. The idea of subtracting, or more correctly adding the negative of, velocities is what is done to calculate relative velocities. For example, if your velocity relative to still water is 10 km/h East and the water current is 6 km/h West, your velocity relative to the shore is 10 +(-6) = 4 km/ East. It takes you longer to go the same distance between two fixed points on the shore if you are going against the current and shorter with the current. I am not sure if this is a one or two dimensional relative velocity problem. It depends on what 5.0km [W20.0S] means.

 

[ericcy]

For example, if your velocity relative to still water is 10 km/h East and the water current is 6 km/h West, your velocity relative to the shore is 10 +(-6) = 4 km/ East. It takes you longer to go the same distance between two fixed points on the shore if you are going against the current and shorter with the current. I am not sure if this is a one or two dimensional relative velocity problem. It depends on what 5.0km [W20.0S] means.

If we were to solve for time, like in this question, would we always be expected to use the velocity of the boat relative to the shore and not the water?

 

[ericcy]

And my apologies, the equation pasted in wrong, they did t=5[distance to island]/(40[velocity relative to water]-6[velocity of water relative to shore]=0.15h)

 

[kuruman]

If we were to solve for time, like in this question, would we always be expected to use the velocity of the boat relative to the shore and not the water?

Yes because the distance is between points fixed on the shore. If a car drives from point A to point B in such a manner as to keep abreast of the boat, their travel times will be the same, no?

You did not explain what 5.0km [W20.0S] means.