# Optimizing Boat Trajectory Across a River

• jamesdubya
In summary, the conversation discusses a problem involving a boat at dock A wanting to reach dock B, which are 100m apart with a velocity of 4m/s. The question asks for the direction and time it takes for the boat to reach dock B if its initial velocity is 6m/s and if it aims directly north, where it will land on the other side. The solution involves using vector methods, finding the resultant of two vectors, and using trigonometric functions such as sine and cosine to find the angle and time.
jamesdubya

## Homework Statement

A Boat at Dock A wants to go to Dock B Straight across. Docks are 100m Apart. Vh=4m/s
A) If Vo1m=6m/s find the direction he must aim boat (theta) to go straight to dock B
B)Find time it takes to get to dock B
C)If he aims boat directly north where will he land on the other side
-------------------Dock B----------------------
Vh=4m/s~~~~~~~~~~~~~~~~~~~~~~~~ |
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 100m
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
~~~~~~~~~~~~Boat ~~~~~~~~~~~~~ |
-------------------Dock A----------------------

## Homework Equations

A) I truly have no idea
B)Vf=Vi+at maybe?
C)Once again, if I knew I would probably have more luck

## The Attempt at a Solution

I wish I knew enough to attempt it..
Thank you for any help you can offer! I am more interested in methods rather than answers

Use vector method.
One vector is Vh from west to east. Other vector is velocity of the boat. The resultant of these two vectors should be along north. two vectors are given. Find the resultant.

Ok so is that something like 24/100? I multiplied the velocities and divided by distance. I'm sorry I am just having a hard time grasping this concept for some reason

When the boat starts moving, the stream pushes it towards east. To move straight towards north, he must aim towards north-west. Draw the vectors and find the angle between V and Vh.

Ok, so then is it something like Tan(4/6) ? I have trouble understanding which to use Cos, Sin, or Tan. I would have a triangle like this http://img121.imageshack.us/img121/341/86596525.jpg right?

Last edited by a moderator:
Your diagram is correct. In the given problem, what is 6 m/s?

the initial velocity of the boat aiming north towards dock b. thank you for your patience

jamesdubya said:
the initial velocity of the boat aiming north towards dock b. thank you for your patience
No. It can't be. If it so, why they ask the angle?
It must be the velocity of the boat in still water.
So in the diagram, diagonal should be 6 m/s.
Find the resultant velocity of the boat towards north.

Pythag. Theor. 6^2+4^2=C^2 = 7.2 north? and then use arcsin6/4 to find the angle? Like i said I am so confused on how to tell what to use and when (as far as sin cos and tan goes) to use them so any quick tip would be much appreciated. I know SohCahToa, but in this case I just don't understand. I know we are looking for the North vector which is y, which would be sin i believe, but I'm not too sure.

According to Pythag. Theor. it should be 4^2 + Vn^2 = 6^2.
Your angle is correct.

so then it would be 4.5, and the angle is 41.81. I know I said it but could you give me a little tip or something on figuring out when to use sin and all that, because I sort of just guessed because we were looking for Y and sin is usually going with Y. So then to find time i would just
divide 100/4.5 ?

Depending on the given quantities, you have to select either sin or cos. In the given problem, opposite side and hypotenuse with respect to the required angle is given. So you have to use sin to find the angle.
Your time is correct.

Thank you, you have been a huge help! I understand it now, it really isn't a difficult question at all.

## 1. How does a boat go across a river?

A boat goes across a river by using the force of the water to propel it forward. The boat's motor or oars create a force that pushes against the water, moving the boat in the desired direction.

## 2. How do you calculate the speed of a boat going across a river?

The speed of a boat going across a river is calculated by dividing the distance traveled by the time it takes to travel that distance. This can be affected by the speed of the current and the boat's motor or oars.

## 3. How do you steer a boat going across a river?

To steer a boat going across a river, the captain or operator must use the boat's rudder to change the direction of the boat. This can be done manually or with the use of a steering wheel or joystick.

## 4. How does the current of a river affect a boat going across it?

The current of a river can affect a boat going across it by either helping or hindering the boat's speed. If the current is flowing in the same direction as the boat, it can help increase its speed. However, if the current is flowing in the opposite direction, it can slow the boat down and make it more difficult to navigate.

## 5. How do you account for wind when navigating a boat across a river?

Wind can play a significant role in navigating a boat across a river. The captain or operator must adjust the boat's course and speed to compensate for the wind's direction and strength. They may also use additional equipment, such as sails, to take advantage of the wind and help move the boat forward.

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