Physics, 19.01.2021 19:00 LarryJoeseph

You're driving down the highway late one night at 20 m/s when a deer steps onto the road 39 m in front of you. Your reaction time before stepping on the brakes is 0.50 s , and the maximum deceleration of your car is 11 m/s2. a. How much distance is between you and the deer when you come to a stop?
b. What is the maximum speed you could have and still not hit the deer?

Answers: 3

Show answers

Answers

Answer from: Svetakotok

a) 10.8 m

b) 24.3 m/s

Explanation:

In order to get the total distance traveled since you see the deer till the car comes to an stop, we need to take into account that this distance will be composed of two parts.The first one, is the distance traveled at a constant speed, before stepping on the brakes, which lasted the same time that the reaction time, i.e., 0.5 sec.We can find this distance simply applying the definition of average velocity, as follows:

$\Delta x_{1} = v_{1o} * t_{react} = 20 m/s * 0.5 s = 10 m (1)$

The second part, is the distance traveled while decelerating at -11 m/s2, from 20 m/s to 0.We can find this part using the following kinematic equation (assuming that the deceleration keeps the same all time):

$v_{1f} ^{2} - v_{1o} ^{2} = 2* a* \Delta x (2)$

where v₁f = 0, v₁₀ = 20 m/s, a = -11 m/s².Solving for Δx, we get:

$\Delta x_{2} = \frac{-(20m/s)^{2}}{2*(-11m/s)} = 18.2 m (3)$

So, the total distance traveled was the sum of (1) and (3):Δx = Δx₁ + Δx₂ = 10 m + 18.2 m = 28.2 m (4)Since the initial distance between the car and the deer was 39 m, after travelling 28.2 m, the car was at 10.8 m from the deer when it came to a complete stop.

We need to find the maximum speed, taking into account, that in the same way that in a) we will have some distance traveled at a constant speed, and another distance traveled while decelerating.The difference, in this case, is that the total distance must be the same initial distance between the car and the deer, 39 m.⇒Δx = Δx₁ + Δx₂ = 39 m. (5)Δx₁, is the distance traveled at a constant speed during the reaction time, so we can express it as follows:

$\Delta x_{1} = v_{omax} * t_{react} = 0.5* v_{omax} (6)$

Δx₂, is the distance traveled while decelerating, and can be obtained using (2):

$v_{omax} ^{2} = 2* a* \Delta x_{2} (7)$

Solving for Δx₂, we get:

$\Delta x_{2} = \frac{-v_{omax} ^{2} x}{2*a} = \frac{-v_{omax} ^{2}}{(-22m/s2)} (8)$

Replacing (6) and (8) in (5), we get a quadratic equation with v₀max as the unknown.Taking the positive root in the quadratic formula, we get the following value for vomax:v₀max = 24.3 m/s.

Answer from: Quest

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

so, refractive index of medium = 300000/200000 = 1.5

1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

∞ refractive index is usually for opaque mediums. so third medium is opaque medium.

Answer from: Quest

Ibelieve the answer is b

Another question on Physics

Physics, 22.06.2019 00:00

What must be the same for any two resistors that are connected in series ? a. the potntial diffrence across each b. the rate at which charge moves through each c. the rate at which energy is used by each d. the resistance to the flow of charge of each

Answers: 1

Answer

Physics, 22.06.2019 12:10

Light traveling in water, nwater = 1.33, strikes a plastic block at an angle of incidence of 51.4°; part of the beam is reflected and part is refracted. if the index of refraction of the plastic is 2.0, what is the angle made by the reflected and refracted beams?

Answers: 2

Answer

Physics, 22.06.2019 14:30

Lightning is an example of what phenomenon? a release of a large amount of energyan absorption of a large amount of energya natural electric circuita natural electric current

Answers: 1

Answer

Physics, 22.06.2019 18:30

Arailroad car collides with and sticks to an identical railroad car that is initially at rest. after the collision, the total kinetic energy of the two cars is a) the same as before. b) half as much as before. c) one third as much as before. d) one fourth as much as before. e) twice as much as before.

Answers: 1

Answer

You know the right answer?

You're driving down the highway late one night at 20 m/s when a deer steps onto the road 39 m in fro...

Questions