A child pulls a rope attached to a stone with a force of `80N`. The rope makes and angle of `40^(@)` to the ground. (i) Calculate the effective value of the pull tending to move the stone along the ground. (ii) Calculate the force tending to lift the stone.

Answer

To solve the problem, we need to break down the force exerted by the child into its horizontal and vertical components. The force applied is 80 N at an angle of 40 degrees to the ground.

### Step 1: Identify the components of the force
The force can be resolved into two components:
- Horizontal component (F_horizontal) which tends to move the stone along the ground.
- Vertical component (F_vertical) which tends to lift the stone.

### Step 2: Calculate the horizontal component
The horizontal component can be calculated using the cosine function:
\[ F_{\text{horizontal}} = F \cdot \cos(\theta) \]
Where:
- \( F = 80 \, \text{N} \) (the force applied)
- \( \theta = 40^\circ \) (the angle with the ground)

Plugging in the values:
\[ F_{\text{horizontal}} = 80 \cdot \cos(40^\circ) \]

Using a calculator:
\[ F_{\text{horizontal}} = 80 \cdot 0.7660 \approx 61.28 \, \text{N} \]

### Step 3: Calculate the vertical component
The vertical component can be calculated using the sine function:
\[ F_{\text{vertical}} = F \cdot \sin(\theta) \]

Plugging in the values:
\[ F_{\text{vertical}} = 80 \cdot \sin(40^\circ) \]

Using a calculator:
\[ F_{\text{vertical}} = 80 \cdot 0.6428 \approx 51.42 \, \text{N} \]

### Final Answers:
(i) The effective value of the pull tending to move the stone along the ground is approximately **61.28 N**.

(ii) The force tending to lift the stone is approximately **51.42 N**.

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