Finding the resultant velocity?

[Math9999]

Homework Statement

A boat heads north across a river at a rate of 4 miles per hour. If the current is flowing east at a rate of 3 miles per hour, find the resultant velocity of the boat.

Homework Equations

None.

The Attempt at a Solution

I know that the resultant velocity is the hypotenuse, which means that 4^2+3^2=v^2, where v=5 mi/h. And that's only part of the answer. The whole answer in the textbook says 5 mi/h at an angle of ≈53.13° to the bank. But how do I find the angle to the bank?

 

[fresh_42]

Homework Statement

A boat heads north across a river at a rate of 4 miles per hour. If the current is flowing east at a rate of 3 miles per hour, find the resultant velocity of the boat.

Homework Equations

None.

The Attempt at a Solution

I know that the resultant velocity is the hypotenuse, which means that 4^2+3^2=v^2, where v=5 mi/h. And that's only part of the answer. The whole answer in the textbook says 5 mi/h at an angle of ≈53.13° to the bank. But how do I find the angle to the bank?

Not without additional assumptions or conditions. You need to interpret "across the river" as perpendicular to the banks.

 

[PeroK]

Homework Statement

A boat heads north across a river at a rate of 4 miles per hour. If the current is flowing east at a rate of 3 miles per hour, find the resultant velocity of the boat.

Homework Equations

None.

The Attempt at a Solution

I know that the resultant velocity is the hypotenuse, which means that 4^2+3^2=v^2, where v=5 mi/h. And that's only part of the answer. The whole answer in the textbook says 5 mi/h at an angle of ≈53.13° to the bank. But how do I find the angle to the bank?

Have you drawn a diagram?

 

[Math9999]

Well, the problem didn't mention as perpendicular to the bank. So that means the answer is just 5 mi/h, right?

 

[PeroK]

Well, the problem didn't mention as perpendicular to the bank. So that means the answer is just 5 mi/h, right?

A velocity always has a direction.

 

[Math9999]

So how to figure the angle out?

 

[fresh_42]

So how to figure the angle out?

By the assumption I've suggested and the diagram @PeroK has suggested. Figure out the remaining angles of your triangle.

 

[Math9999]

cos^-1(3/5)≈53.13°, am I right?

 

[PeroK]

cos^-1(3/5)≈53.13°, am I right?

I suspect your calculator can tell you that!

 

[Math9999]

Okay, thank you!