After making weather observations and obtaining a weather briefing, the instructor pilot (IP) briefed the chase crew of the expected northerly track. The IP and student took off at 0705 CST and ascended to 1200 to 15000 ft AGL and began tracking north-northwest. After several antennas were noted downwind, an ascent was made to 3200 ft AGL and the balloon moved easterly. After descending, it tracked due north. The balloon proceeded into an area of unfavorable terrain with no east-west roads. Also, the sky condition became hazy and the IP believed the chase crew would have difficulty following; therefore, they continued for a recovery near a major road. Meanwhile, the wind picked up to 20 mph. At about 0920, a landing was made near a highway in an area covered with mesquite. During the landing, contact was made with several of the mesquite, a fence, and the ground. The envelope also brushed against a power line. The student was injured during the landing.