Final answer:
To maintain a constant speed of 10.8 m/s while rounding a curve of radius 10.8 m, a 66.5 kg sprinter must exert an extra force of 66.66 N on the ground.
Step-by-step explanation:
To find the extra force a sprinter must exert on the ground to round a curve of radius 10.8 m while running at a constant speed of 10.8 m/s, we need to calculate the centripetal force required. The formula for centripetal force (Fc) is Fc = (mv²)/r, where m is the mass, v is the velocity, and r is the radius of the curve.
Plugging the given values into the formula:
Fc = (66.5 kg × (10.8 m/s)²) / 10.8 m
Fc = (66.5 kg × 116.64 m²/s²) / 10.8 m
Fc = 719.92 kg·m/s² / 10.8 m
Fc = 66.66 N
Therefore, the sprinter must exert an extra force of 66.66 N on the ground to maintain his motion around the curve without changing his speed.