A ranger in a national park is driving at 11.8mi / h when a deer jumps into the road 242 ft ahead of the vehicle. After a reaction time of t the ranger applies the brakes to produce and acceleration of -9.18ft/s^2 What is the maximum reaction time allowed if she is to avoid hitting the deer? Answer in units of s.

The maximum reaction time is approximately 13 seconds

Explanation:

In order to answer this problem let's start by converting the speed of the ranger's vehicle from miles per hour into feet per second, knowing that 1 mile is the same as 5280 ft and i hour is 3600 seconds:

Now, with this information, we set the equation for the amount of time needed to reduce the speed from 17.3 ft/s to full stop (0 ft/s):

Now, the space covered during these 1.88 s when the vehicle reaches full stop while it decelerates is calculated via:

So, the maximum amount of time the ranger has to react and press the break while driving at 17.3 ft/s is the time to cover 242 ft minus 16.3 ft = 225.7 ft

During 225.7 ft the ranger could be driving in uniform motion (with speed 17.3 ft per second), we find the time to cover such:

gpe = mass x gravity constant x height or… gpe = mgh

where… mass: measured in kilograms (kg)

gravity: gravity constant on earth = 10.00 m/s2

height: measured in meters (m)

gpe: measured in joules (j) or kilojoules (kj)

how do you solve gpe?

gravitational potential energy (gpe) is the energy an object has because of its position above the. ground.

gpe = mass x gravity constant x height or… gpe = mgh.

mass:

note: to earn full marks when solving science word problems, you must show your work:

formula.

example:

given values:

mass = 0.3 kg.