A boy shouts towards a high wall and hears the echo 0.25 s later. The distance between the boy and the wall is 200 m. Calculate the speed of sound.

The first sound travels directly from the boy to the girl, a distance of $200 \, m$, in $0.6 \, s$.

$$v = \frac{\text{Distance}}{\text{Time}} = \frac{200 \, m}{0.6 \, s} = \frac{1000}{3} \, m/s$$

The second sound is heard $0.25 \, s$ after the first sound.

$$t_{second} = t_{first} + 0.25 \, s = 0.6 \, s + 0.25 \, s = 0.85 \, s$$

$$L_{second} = v \times t_{second} = \frac{1000}{3} \, m/s \times 0.85 \, s$$ $$L_{second} = \frac{850}{3} \, m$$ $$L_{second} \approx 283.33 \, m$$

The length of the path followed by the second sound is $\boxed{\text{283.33 m}}$.

9. A person standing out in an illuminated garden at night is observed to have two shadows of different sharpness. Explain this observation.

This observation occurs because there are at least two different light sources illuminating the person. Each light source casts its own shadow. The sharpness of a shadow depends on the size and distance of the light source. A smaller or more distant light source produces a sharper shadow (umbra), while a larger or closer light source produces a less sharp, fuzzy shadow (penumbra). Therefore, the two shadows of different sharpness indicate that the light sources are of different sizes, intensities, or positions.

10. Identify the type of charge induced at X and Y.

When a positively charged metal sphere is brought near an uncharged metallic object, electrostatic induction occurs. The free electrons in the uncharged metallic object are attracted towards the positively charged sphere.

• At point X (closer to the positive sphere), negative charges will accumulate due to the attraction of electrons.
• At point Y (further from the positive sphere), there will be a deficiency of electrons, resulting in an accumulation of positive charges.

Charge at X: $\boxed{\text{Negative}}$
Charge at Y: $\boxed{\text{Positive}}$