The seconds hand of a clock is 2.0 cm long. Displacement of the tip of the hand in 15 s is

Options

A. 2.0 cm
B. `2 sqrt(2)` cm
C. 1.0 cm
D. 0.5 cm

Explanation

To find the displacement of the tip of the second hand of a clock in 15 seconds, follow these steps:

### Step 1: Understand the motion of the second hand
The second hand of a clock completes one full revolution (360 degrees) in 60 seconds. Therefore, in 15 seconds, it will move through a fraction of this circle.

**Hint:** Calculate the angle covered by the second hand in 15 seconds.

### Step 2: Calculate the angle moved in 15 seconds
The second hand moves at a rate of 360 degrees per 60 seconds. Thus, in 15 seconds, the angle moved is:
\[ \text{Angle} = \left(\frac{360 \text{ degrees}}{60 \text{ seconds}}\right) \times 15 \text{ seconds} = 90 \text{ degrees} \]

**Hint:** Remember that 90 degrees corresponds to a quarter of a full circle.

### Step 3: Visualize the displacement
The displacement is the straight line distance from the initial position of the tip of the second hand to its final position after 15 seconds. The initial and final positions form a right triangle with the radius of the circle as the two legs.

**Hint:** Draw a diagram to visualize the initial and final positions of the second hand.

### Step 4: Use the Pythagorean theorem
Let the length of the second hand (radius) be \( r = 2.0 \, \text{cm} \). The two legs of the right triangle formed by the initial and final positions of the second hand are both equal to the length of the second hand:
- OA = 2.0 cm (initial position)
- OB = 2.0 cm (final position)

According to the Pythagorean theorem:
\[ AB^2 = OA^2 + OB^2 \]
Substituting the values:
\[ AB^2 = (2.0 \, \text{cm})^2 + (2.0 \, \text{cm})^2 = 4.0 + 4.0 = 8.0 \]
\[ AB = \sqrt{8.0} = 2.83 \, \text{cm} \]

**Hint:** Make sure to calculate the square root correctly to find the displacement.

### Step 5: Conclusion
The displacement of the tip of the second hand in 15 seconds is approximately \( 2.83 \, \text{cm} \).

**Final Answer:** The displacement of the tip of the second hand in 15 seconds is \( 2.83 \, \text{cm} \).