Question

5. Amy and Josh are coasting on their bicycles down a 10° slope at 15 m/s through still air. The mass of Amy and her bicycle is 60 kg. The mass of Josh and his bicycle is 90 kg. The cross-sectional area of Amy and her bicycle is 0.45, while the cross-sectional area of Josh and his bicycle is 0.60. The drag coefficient for both cyclists is 0.70. Other than gravity and air resistance, the external forces acting on the two bicycle and rider systems are the same. Which cyclist is more affected by air resistance? The Answer is Amy but what is the math invovled, Please Show Work and Help!

Answer 1

Forces in the x-direction:

$ma = mg*sin \theta - cA v^{2}$

The acceleration:
$a = g*sin \theta - \frac{cA}{m} v^2$

The first term is independent of mass, only the second term depends on mass m:
$\frac{cA}{m} v^2$
Amy:
$\frac{0.45 * 0.7}{60} v^2 = 0.00525v^2$
Josh:
$\frac{0.6 * 0.7}{90} v^2 = 0.00467v^2$

The negative impact on Amy is larger than on Josh.