A ship is moving due east with a velocity of 12 m/ sec, a truck is moving across on the ship with velocity 4 m/sec. A monkey is climbing the vertical pole mounted on the truck with a velocity of 3m/sec. Find the velocity of the monkey as observed by the man on the shore

Options

A. 10 m/sec
B. 15 m/sec
C. 13 m/sec
D. 20 m/sec

Answer

To find the velocity of the monkey as observed by the man on the shore, we need to consider the velocities of the ship, truck, and monkey in a three-dimensional coordinate system. Let's break down the problem step by step:

### Step 1: Define the Directions and Velocities
- The ship is moving due east with a velocity of \( v_x = 12 \, \text{m/s} \).
- The truck is moving across the ship (let's assume this is in the north direction) with a velocity of \( v_y = 4 \, \text{m/s} \).
- The monkey is climbing the vertical pole on the truck with a velocity of \( v_z = 3 \, \text{m/s} \).

### Step 2: Identify the Components of Velocity
We have the following components of the velocity:
- \( v_x = 12 \, \text{m/s} \) (east direction)
- \( v_y = 4 \, \text{m/s} \) (north direction)
- \( v_z = 3 \, \text{m/s} \) (upward direction)

### Step 3: Calculate the Resultant Velocity
To find the resultant velocity of the monkey as observed from the shore, we will use the Pythagorean theorem in three dimensions. The resultant velocity \( v \) can be calculated using the formula:
\[ v = \sqrt{v_x^2 + v_y^2 + v_z^2} \]

### Step 4: Substitute the Values
Now, substitute the values into the equation:
\[ v = \sqrt{(12)^2 + (4)^2 + (3)^2} \]
Calculating each term:
- \( (12)^2 = 144 \)
- \( (4)^2 = 16 \)
- \( (3)^2 = 9 \)

### Step 5: Sum the Squares
Now, sum these values:
\[ v = \sqrt{144 + 16 + 9} = \sqrt{169} \]

### Step 6: Calculate the Square Root
Finally, calculate the square root:
\[ v = 13 \, \text{m/s} \]

### Conclusion
The velocity of the monkey as observed by the man on the shore is \( 13 \, \text{m/s} \).

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