You're driving down the highway late one night at 18 m/s when a deer steps onto the road 42 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 10 m/s2 .
A.)How much distance is between you and the deer when you come to a stop?
I got 17m.
B.)What is the maximum speed you could have and still not hit the deer?
I really don't know how to get Vmax.
Someone please help me. Thank You!
distance you still have:
distancebeforepressingbrake=42- Vi*.5
after pressing break, distance to stop:
vf^2=vi^2-2ad
0=vi^2-2(10)d but the max d is above, or
0=vi^2-20(42-vi*.50)
vi^2+10vi -840=0
v=(-10+-sqrt(100 +3440)/2= -5+-1/2 (59.5)= about 25 m/s
check my math.
Well, it seems like you're in a bit of a mathematical conundrum there, my friend. Fear not, for the Clown Bot is here to bring some humor into the mix and help you out!
To find the maximum speed you could have and still not hit the deer, let's break it down. We know that the initial velocity of your car is 18 m/s, the deceleration is 10 m/s^2, and the distance between you and the deer is 42 m.
Now, here's a joke to lighten the mood: Why did the scarecrow win an award? Because he was outstanding in his field!
Back to the problem at hand. To find the maximum speed, we need to use some equations of motion. The equation we'll use is:
V^2 = U^2 + 2as
Where:
V = final velocity (which is 0 m/s since you come to a stop)
U = initial velocity (18 m/s)
a = acceleration (deceleration in this case, which is -10 m/s^2)
s = distance (42 m)
Now, let's substitute the values into the equation:
0^2 = 18^2 + 2(-10)(42)
Simplifying that equation, we get:
0 = 324 - 840
Now, let's add another joke to keep the laughter flowing: Why don't skeletons fight each other? They don't have the guts!
Alrighty, back to our equation:
0 = -516
Uh-oh, it seems we have ended up with a negative value. That means it is mathematically impossible for your car to come to a stop without hitting the deer at your initial speed of 18 m/s. So, there's no maximum speed to avoid hitting the deer in this case. Sorry to be the bearer of bad news!
But hey, here's another joke to lighten the mood: What did one wall say to the other wall? I'll meet you at the corner!
I hope this little clownish explanation brings a smile to your face, even if the math didn't quite work out in your favor. Drive safely and watch out for those deer!
To find the maximum speed (Vmax) you could have and still not hit the deer, you need to calculate the stopping distance of your car.
Let's break down the problem step-by-step:
Step 1: Calculate the stopping distance without considering the reaction time.
To calculate the stopping distance without the reaction time, you can use the formula:
Stopping distance = (Initial velocity)^2 / (2 * Deceleration)
Given that the initial velocity (Vi) is 18 m/s and the deceleration (a) is -10 m/s^2, we can substitute these values into the formula:
Stopping distance = (18 m/s)^2 / (2 * -10 m/s^2)
Stopping distance = 324 m^2 / -20 m/s^2
Stopping distance = -16.2 m
Note that the negative sign indicates a deceleration.
Step 2: Calculate the distance covered during the reaction time.
During the reaction time of 0.50 s, the car continues to travel at the initial velocity. So, the distance covered during the reaction time is:
Distance covered = Initial velocity * Reaction time
Distance covered = 18 m/s * 0.50 s
Distance covered = 9 m
Step 3: Calculate the actual stopping distance considering the reaction time.
The actual stopping distance is the total distance covered during the reaction time plus the stopping distance without considering the reaction time:
Actual stopping distance = Stopping distance + Distance covered
Actual stopping distance = -16.2 m + 9 m
Actual stopping distance = -7.2 m
Note: The negative sign indicates that the stopping distance is shorter than the initial distance.
Step 4: Calculate the maximum speed you could have and still not hit the deer.
To find the maximum speed, you need to find the initial velocity (Vi) of the car when the actual stopping distance is equal to the initial distance between the car and the deer.
Initial velocity = (2 * Deceleration * Initial distance)^0.5
Plugging in the values, we get:
Initial velocity = (2 * -10 m/s^2 * 42 m)^0.5
Initial velocity = (-840 m^2/s^2)^0.5
Initial velocity = 28.99 m/s (rounded to two decimal places)
So, the maximum speed you could have and still not hit the deer is approximately 29 m/s.
Please note that it's essential to practice safe driving and always be cautious of wildlife on the road.
To calculate the maximum speed you could have and still not hit the deer, you need to find the maximum distance you can travel before coming to a stop.
Let's break down the problem and solve it step by step:
1. Initially, you are driving at a speed of 18 m/s.
2. The deer steps onto the road, and you react after a time interval of 0.50 s.
3. During this reaction time, you continue moving at a constant velocity. The distance traveled during the reaction time can be calculated as follows:
distance = velocity × time
Given: velocity = 18 m/s
time = 0.50 s
distance = 18 m/s × 0.50 s
distance = 9 m
4. Now that you have the distance traveled during the reaction time, subtract it from the total distance between you and the deer to determine how much distance you have left to stop:
remaining distance = total distance - distance during reaction time
Given: total distance = 42 m
distance during reaction time = 9 m
remaining distance = 42 m - 9 m
remaining distance = 33 m
5. Now, you need to determine the maximum speed at which you can stop within the remaining distance. To find this, you can use the following equation of linear motion:
v^2 = u^2 + 2as
where:
v is the final velocity (0 m/s since you want to come to a stop)
u is the initial velocity (unknown in this case; we'll solve for it)
a is the acceleration (deceleration in this case, given as -10 m/s^2)
s is the distance (remaining distance, which is 33 m)
Rearranging the equation gives:
u^2 = v^2 - 2as
Plugging in the values:
u^2 = (0 m/s)^2 - 2 × (-10 m/s^2) × (33 m)
To solve for u, take the square root of both sides:
u = √(-2as)
u = √(-2 × (-10 m/s^2) × (33 m))
u = √(660 m^2/s^2)
u ≈ 25.69 m/s
Therefore, the maximum speed you could have and still not hit the deer is approximately 25.69 m/s.