Jim asked in Science & MathematicsPhysics · 7 years ago

# If a 1,100kg car at 30 m/s hits a 10kg stationary deer, what acceleration does the deer experience?

m/s = meters per second (roughly 70 mph)

Also what force is that on the deer? Is it more than gravity?

How slow would you have to be travelling in the car for the force to be less than gravity on the deer?

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• 7 years ago

This happened to me about 6 years ago. Immediately after the car hits the deer, the deer is stuck to the front of the car.

This is a conservation of momentum problem.

Initial momentum of car = 1100 * 30, Initial momentum of deer = 0

After the car hits the deer, the total mass = 1100 + 10 = 1110 kg

Final momentum of car and deer = 1110 * vf

1110 * vf = 1100 * 30

vf = (1100 * 30) ÷ 1110 ≈ 29.73 m/s

Immediately after the car hits the deer, the velocity of the car and deer is approximately 29.73 m/s.

During the collision, the car’s velocity decreased from 30 m/s to 29.73 m/s; and the deer’s velocity increased from 0 m/s to 29.73 m/s.

Acceleration = (vf – vi) ÷ t

To determine the acceleration and force, you need to know the amount of time which passed as the velocities changed.

Let’s assume that the collision occurred during a 2 second time period.

Acceleration of deer = (29.73 – 0) ÷ 2 = 14.865 m/s^2

Force = m * a = 10 * 14.865 = 148.65 N

Is it more than gravity? Gravity is acceleration, not a force. Weight is the force, which is caused by gravity.

Weight = mass * g, g = 9.8 m/s^2

The acceleration of the deer, 14.865 m/s^2

Yes, the acceleration of the deer is greater than the gravitational acceleration.

How slow would you have to be travelling in the car for the force to be less than gravity on the deer?

To determine the velocity of the car, before the collision, you have to work the problem backwards!

Force = m * a = m * (vf – vi) ÷ t

For the deer, m = 10, vi = 0 m/s, t = 2 seconds

Force = 10 * (vf – 0) ÷ 2

Force = 10 * vf ÷ 2

The force, which is caused by gravity is the weight of the object.

Weight of deer = 98 N

98 = 10 * vf ÷ 2

Multiply both sides by 2

196 = 10 * vf, vf = 19.6 m/s

This is the velocity of the deer immediately after the collision. Immediately after the collision, the deer is stuck to the front of the car, So, the car’s velocity immediately after the collision, is 19.6 m/s.

Now we do a momentum problem.

Immediately after the collision, momentum of car and deer = 1110 * 19.6

Before the collision, momentum of car = 1100 * vi and momentum of deer = 0.

1100 * vi = 1110 * 19.6

vi = 1110 * 19.6 ÷ 1100 ≈ 19.78 m/s

This is the required velocity of the car before the collision, if the acceleration of deer is only 9.8 m/s^2!

All of this numbers are based on the assumption that the collision occurred in 2 seconds!

I hope this helps!

• latner
Lv 4
3 years ago

you imagine hitting deer is undesirable? attempt hitting a black angus bull, now that critter does some harm to a motor vehicle plus there's a sturdy danger that the passengers contained in the vehicle will be heavily harm. Been there....accomplished that..... do not favor to do it again!!!!!!