Question

A person is driving down a country lane at 25 m/s, when a deer suddenly jumps in front of the car. The deer is 75 m ahead and when the driver hits the brakes, the car slows at a rate of 4.20 m/s each second. Does the car hit the deer?

Answer 1

We can use the equation for Newtons third law.

fv² - iv² = 2as

Variables:

fv = final velocity (0)

iv = inital velocity (25)

s = distance traveled (?)

a = acceleration (-4.2)

We are given all variables except "s".

Solve for s:

fv² - iv² = 2as

0² - 25² = 2(-4.2)s

625 = -8.4s

74.4 ≈ s

Since 74.4 < 75, the car does not hit the deer.

Best of Luck!

Answer 2

Answer:

The car does not hit the deer.

Explanation:

In order to find out, whether the car stops before hitting the dear or not, we will use 3rd equation of motion.

2as = Vf² - Vi²

where,

s = distance covered by car before stopping = ?

a = deceleration of car = - 4.2 m/s²

Vf = Final Velocity of the Car = 0 m/s (Since, the car finally stops)

Vi = Initial Velocity of the Car = 25 m/s

Therefore,

2(- 4.2 m/s²)s = (0 m/s)² - (25 m/s)²

s = (- 625 m²/s²)/(-8.4 m/s²)

s = 74.4 m

So, the car stops in 74.4 m, while the deer is at a distance of 75 m.

Hence, the car does not hit the deer.