A sleepy man drives a car along a straight section of highway at a constant speed of 89.6 km/h. His eyes begin to close, and his car moves at an angle of 4.90° relative to the road. For how long can his attention lapse before the car begins to move across the lane divider, originally 1.09 m from the side of the car?

Question

A sleepy man drives a car along a straight section of highway at a constant speed of 89.6 km/h. His eyes begin to close, and his car moves at an angle of 4.90° relative to the road. For how long can his attention lapse before the car begins to move across the lane divider, originally 1.09 m from the side of the car?

Answer 1

The transverse velocity component is

89.6 sin4.9 = 7.653 km/h = 2.126 m/s

He will hit the lane diver after
t = 1.09/2.126 = 0.51 seconds

Answer 2

To solve this problem, we need to break it down into two components: the distance traveled by the car and the distance between the car and the lane divider.

First, let's determine the distance traveled by the car during the inattentive period. We can use the formula: Distance = Speed x Time.

Given that the speed of the car is 89.6 km/h, we need to convert it to m/s:
Speed = 89.6 km/h * (1000 m / 1 km) * (1 h / 3600 s)
= 24.89 m/s

Let's assume that the time given is the duration of the man's attention lapse. We'll call it "t" (in seconds).
So, the distance traveled during this time can be calculated as:
Distance_traveled = Speed x t

Now, let's calculate the distance between the car and the lane divider. We know that the car moves at an angle of 4.90° relative to the road and the initial distance between the car and the side of the car is 1.09 m.

To find the distance between the car and the lane divider, we use trigonometry. The distance can be represented as:
Distance_car_lane = initial_distance_from_car * tan(angle)

Distance_car_lane = 1.09 m * tan(4.90°)

Now, we need to compare the distance traveled by the car with the distance between the car and the lane divider. If the distance traveled is greater than the distance between the car and the lane divider, the car will cross the lane divider.

So, to find the maximum time the man's attention can lapse before the car starts to cross the lane divider, we need to solve the inequality:
Distance_traveled > Distance_car_lane

24.89 m/s * t > 1.09 m * tan(4.90°)

Simplifying this inequality, we can calculate the maximum value of "t".