Final answer:
The altitude of the Sun along the meridian on the first day of summer is 67° above the horizon for someone at the equator, as on this day, the Sun's declination is 23° north of the celestial equator.
Step-by-step explanation:
The altitude of the Sun along the meridian on the first day of summer, known as the summer solstice which occurs on or about June 21, can be calculated based on the Sun's declination on that day.
For someone located on the equator, the Sun's declination is 23° north of the celestial equator, which means it will be 23° away from the zenith (the point directly overhead) at noon. To find the altitude of the Sun, you subtract the declination from the altitude of the zenith, which is 90°.
The calculation would be 90° - 23° = 67° above the horizon.
This phenomenon occurs because, on the first day of summer, the Sun shines directly upon the Northern Hemisphere, particularly at the latitude known as the Tropic of Cancer, which is 23° N latitude. At this latitude, the Sun is directly overhead at noon.