Explanation:
First, find the distance she travels before reacting:
Δx = v₀ t + ½ at²
Δx = (17.0 m/s) (1.6 s) + ½ (0 m/s²) (1.6 s)²
Δx = 27.2 m
Now find the distance she travels before stopping:
v² = v₀² + 2aΔx
(0 m/s)² = (17.0 m/s)² + 2 (-4.9 m/s²) Δx
Δx = 29.5 m
The total distance traveled is:
27.2 m + 29.5 m = 56.7 m
56.7 m is less than 65 m, so yes, she can avoid hitting the child.
