To find the displacement of the child, we'll break down the problem using vector analysis.

Step 1: Represent the problem with vectors

1. Vector from the slide to the lemonade stand:

   • Magnitude: $50 \, \text{m}$
   • Bearing: $120^\circ$
   • This means the vector makes an angle of $120^\circ - 90^\circ = 30^\circ$ with the negative x-axis (assuming the positive x-axis is 0°).

   The components of this vector (using the fact that bearing angles are measured clockwise from the North): $\text{Vector A}_x = 50 \times \cos(120^\circ) = 50 \times (-0.5) = -25 \, \text{m}$ $\text{Vector A}_y = 50 \times \sin(120^\circ) = 50 \times \left(\frac{\sqrt{3}}{2}\right) \approx 50 \times 0.866 = 43.3 \, \text{m}$

2. Vector from the lemonade stand to the ice cream truck:

   • Magnitude: $30 \, \text{m}$
   • Bearing: $170^\circ$
   • The angle with the positive x-axis would be $170^\circ - 90^\circ = 80^\circ$.

   The components of this vector are: $\text{Vector B}_x = 30 \times \cos(170^\circ) = 30 \times (-0.985) \approx -29.55 \, \text{m}$ $\text{Vector B}_y = 30 \times \sin(170^\circ) = 30 \times 0.174 \approx 5.22 \, \text{m}$

Step 2: Find the resultant vector

To find the displacement vector, we add the components of the two vectors:

• Resultant x-component: $R_x = -25 + (-29.55) = -54.55 \, \text{m}$

• Resultant y-component: $R_y = 43.3 + 5.22 = 48.52 \, \text{m}$

Step 3: Calculate the magnitude of the resultant vector

The magnitude of the displacement is given by: $\text{Displacement} = \sqrt{R_x^2 + R_y^2}$ $\text{Displacement} = \sqrt{(-54.55)^2 + (48.52)^2} \approx \sqrt{2973.7 + 2354.1} \approx \sqrt{5327.8} \approx 73.00 \, \text{m}$

Final Answer:

The correct answer is: a) 73.00 m

Would you like more details on any part of this solution or have any other questions? Here are some related questions you might find helpful:

1. How do you calculate the angle between two vectors?
2. What is the difference between distance and displacement?
3. How do you resolve a vector into its components?
4. How do bearings work in navigation?
5. What are some examples of vector addition in real life?

Tip: When dealing with vector problems, always break down vectors into their components and use trigonometry to handle bearings effectively.