You're driving down the highway late one night at 16m/s when a deer steps onto the road 44m in front of you. your reaction time before stepping on the brakes is 0.50s , and the maximum deceleration of your car is 10m/s2 .

how much distance is between you and the deer? what is the maximum speed you could have and still not hit the deer?

Part a)

d = 23.2 m

Part b)

v = 25.1 m/s

Explanation:

Part a)

As we know that the speed of the car is given as

reaction time of the driver = 0.50 s

now the distance moved by the car during reaction time

After this car is decelerated due to brakes with deceleration

so the distance moved by the car till it will stop

so total distance moved by the car

Now the distance between the car and deer is given as

Part b)

Let the driver is moving with speed "v"

now the distance moved in reaction time

now after applying brakes the distance moved by it

so we have

so total distance covered is given as

for maximum speed v the distance moved is

so we have

by solving above equation we have

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y