You are driving down a highway at a speed of 20.0m/s when you spot a deer. You quickly slam on your brakes, trying to stop your car in front of the deer. Assume the braking force can be modeled as kinetic friction with a friction coefficient of 0.80. If the deer was 75.0m away from you when you slam on your brakes, will you hit the deer? If you do, find the speed at which you hit it. If you don't, find how far from the deer you stop
u = a/g = 0.8
a = 0.8*g = 0.8 * (-9.8) = -7.84 m/s^2
d = (V^2-Vo^2)/2a = (0-(20^2)/-15.68 =
25.5 m. To stop.
75-25.5 = 49.5 m. from deer.
In order to determine whether you will hit the deer or not, we need to analyze the situation using the laws of motion and calculate the stopping distance based on the given information.
To determine if you hit the deer, we need to find the stopping distance and compare it to the initial distance from the deer.
Step 1: Convert the given speed from m/s to km/h for consistency.
20.0 m/s * (3.6 km/h / 1 m/s) = 72.0 km/h
Step 2: Calculate the stopping distance.
The stopping distance can be determined using the equation:
stopping distance = (initial velocity^2) / (2 * acceleration)
The acceleration can be found using the equation:
acceleration = friction coefficient * gravitational acceleration
Given:
initial velocity (u) = 20.0 m/s
friction coefficient (μ) = 0.80
gravitational acceleration (g) = 9.8 m/s^2 (approximate value)
acceleration = 0.80 * 9.8 = 7.84 m/s^2
stopping distance = (20.0^2) / (2 * 7.84) = 51.02 m (approximately)
Step 3: Compare the stopping distance to the initial distance from the deer.
If the stopping distance is greater than or equal to the initial distance (75.0 m), you will hit the deer. If it is less, you will be able to stop before hitting the deer.
In this case, the stopping distance (51.02 m) is less than the initial distance (75.0 m), so you will be able to stop before hitting the deer.
Step 4: Calculate the final speed when you stop.
To find the final speed, we can use the equation:
final velocity (v) = √(initial velocity^2 - 2 * acceleration * stopping distance)
v = √(20.0^2 - 2 * 7.84 * 51.02) = √(400 - 807.04) = √(-407.04) (approximately)
Since the result is imaginary, which implies a negative velocity, it means the car will come to a stop before reaching the deer and you won't hit it.
Therefore, you will stop at a distance less than 75.0 m from the deer, but won't hit it.
Note: The calculations assume constant acceleration throughout the braking process and idealized conditions. Real-world factors, such as driver reaction time and variations in friction, can affect the actual stopping distance.