River question (looking for angles and headings)

[alexi_b]

Homework Statement

A child in danger of drowning in a river is being carried downstream by a current that has a speed of 2.35km/h. The child is 0.505km from shore and 0.780km upstream of a boat landing when a rescue boat sets out. If the boat proceeds at its maximum speed of 18.8km/h relative to the water,
a) what heading relative to the shore should the captain take?
b)What angle (in degrees) does the boat velocity make with the shore?

Homework Equations

The Attempt at a Solution

for a) i just tried using the inverse of tan of (0.6/0.8) but apparently its not right
for b) I thought if the angle found in a was right, i could find the velocity components and subtract the velocity of the river from the y-direction and put those values into a right angled triangle to solve for the angle but that didnt work either

 

[haruspex]

inverse of tan of (0.6/0.8)

Where did the 0.6 and 0.8 come from?

It usually helps in such problems to draw a diagram and create variable names for all the data rather than use the numbers. They can be plugged in later.
Let the boat speed be b, the current speed c, the distance from the shore x, and the distance along the stream y. If the boat heads at angle θ to the shore, what are its velocity components relative to the stream?

 

[alexi_b]

Where did the 0.6 and 0.8 come from?

It usually helps in such problems to draw a diagram and create variable names for all the data rather than use the numbers. They can be plugged in later.
Let the boat speed be b, the current speed c, the distance from the shore x, and the distance along the stream y. If the boat heads at angle θ to the shore, what are its velocity components relative to the stream?

Sorry I was referring to another question but it was suppose to be tan inverse of (0.505/0.780). I also don’t get how to visualize it. Is the boat starting on one end of the shore and I have to find the angle it makes relative to the shore across the river?

 

[alexi_b]

Where did the 0.6 and 0.8 come from?

It usually helps in such problems to draw a diagram and create variable names for all the data rather than use the numbers. They can be plugged in later.
Let the boat speed be b, the current speed c, the distance from the shore x, and the distance along the stream y. If the boat heads at angle θ to the shore, what are its velocity components relative to the stream?

And also to add I kept getting 32.9 for my angle for a, which is apparently wrong. I drew it out like you said and my answer is still wrong so do you proposing anything else?

 

[Cutter Ketch]

suppose to be tan inverse of (0.505/0.780)

That is directly toward where the child is relative to the landing right now. The river is moving. The child is moving. It takes time for the boat to get there. You can’t just aim at where the child is, you have to aim at where he will be when the boat finally gets there.

 

[alexi_b]

That is directly toward where the child is relative to the landing right now. The river is moving. The child is moving. It takes time for the boat to get there. You can’t just aim at where the child is, you have to aim at where he will be when the boat finally gets there.

but wouldn't the apply to part b)?

 

[Cutter Ketch]

but wouldn't the apply to part b)?

Yes, I see. You are right

 

[alexi_b]

Yes, I see. You are right

So how do you propose I solve part a)? The only way I could think of is solving using tan inverse

 

[haruspex]

getting 32.9 for my angle for a

That is what I get.
To be clear, "heading" means the angle the boat points. If we assume the boy and boat are equally affected by the current then we can ignore it for part a.
(In reality, though, the current is slow near the shore and at maximum in midstream, but we have no information on that.)
Edit: there is an ambiguity. Is it the angle to the shore in the downstream direction or the upstream direction? Maybe the answer to a should be 147.1 degrees.