A ranger in a national park is driving at 21.8 mi/h when a deer jumps into the road
229 ft ahead of the vehicle. After a reaction time of t the ranger applies the brakes to
produce and acceleration of −8.84 ft/s
2
.
What is the maximum reaction time allowed if she is to avoid hitting the deer?
Answer in units of s.

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.