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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?

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hamzaahmeds

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.
  • Initial velocity=25m/s=u
  • Final velocity=0m/s(As it stopped)=v
  • Deacceleration=a=-4.2m/s^2
  • Distance of deer=75m
  • Distance at where car stops=s

Using third equation of kinematics

[tex]\boxed{\sf v^2-u^2=2as}[/tex]

[tex]\\ \sf\longmapsto (0)^2-(25)^2=2(-4.2)s[/tex]

[tex]\\ \sf\longmapsto -625=-8.4s[/tex]

[tex]\\ \sf\longmapsto 8.4s=625[/tex]

[tex]\\ \sf\longmapsto s=\dfrac{625}{8.4}[/tex]

[tex]\\ \sf\longmapsto s=74.4m[/tex]

  • AS IT IS LESS THAN 75M HENCE CAR DOESNOT HIT THE DEAR.

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