You are a jaywalker at a distance x from an intersection. At time t = 0 you start tocross it at a constant velocity perpendicular to the direction of the street such that it would take you timeT to cross it. Incidentally, at t = 0, there is also a car at X = 40.0 m away from the intersection. It is aself-driving Tesla, and it drives toward the intersection at such a speed that if the light remained green,the car would reach the intersection at t = T .At time t = 0, the light turns red, and since the car is driven by a computer, it immediately beginsdecelerating with constant acceleration a such that it comes to a stop at exactly X = 0.You are x = 8.00 m from the intersection. Do you get hit by the car? If yes, report the speed of the carrelative to the ground when it hits you, as a percent of its original speed before the light turned red. Ifno, report how far away the car is from you when you finish crossing the street
Question
You are a jaywalker at a distance x from an intersection. At time t = 0 you start tocross it at a constant velocity perpendicular to the direction of the street such that it would take you timeT to cross it. Incidentally, at t = 0, there is also a car at X = 40.0 m away from the intersection. It is aself-driving Tesla, and it drives toward the intersection at such a speed that if the light remained green,the car would reach the intersection at t = T .At time t = 0, the light turns red, and since the car is driven by a computer, it immediately beginsdecelerating with constant acceleration a such that it comes to a stop at exactly X = 0.You are x = 8.00 m from the intersection. Do you get hit by the car? If yes, report the speed of the carrelative to the ground when it hits you, as a percent of its original speed before the light turned red. Ifno, report how far away the car is from you when you finish crossing the street
Solution
To solve this problem, we need to first find out the time it takes for the jaywalker to reach the intersection, and then compare it with the time it takes for the car to reach the intersection.
Given:
- Distance of jaywalker from intersection, x = 8.00 m
- Time taken by jaywalker to cross the street, T (unknown)
- Distance of car from intersection, X = 40.0 m
- Time taken by car to reach the intersection if light remained green, T
- Acceleration of car, a (unknown)
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Find the velocity of the jaywalker: Since the jaywalker crosses the street at a constant velocity, we can use the formula v = x/t. But we don't know T yet, so we can't calculate this now.
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Find the initial velocity of the car: The car would reach the intersection at time T if the light remained green, so its initial velocity (v0) is X/T.
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Find the acceleration of the car: The car decelerates to a stop at the intersection, so its final velocity (v) is 0. We can use the formula v = v0 + at to find a. Rearranging, we get a = (v - v0) / t = -v0 / T.
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Find the time it takes for the car to reach the jaywalker: We can use the formula x = v0t + 0.5at^2. Substituting the values we found, we get t = sqrt(2x / a).
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Compare the times: If the time it takes for the car to reach the jaywalker is less than T, then the jaywalker gets hit by the car. If it's greater, then the jaywalker crosses the street safely.
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If the jaywalker gets hit, find the speed of the car when it hits: We can use the formula v = v0 + at. The speed of the car relative to the ground when it hits the jaywalker is then v / v0 * 100%.
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If the jaywalker crosses safely, find how far away the car is: We can use the formula x = v0t + 0.5at^2. The distance of the car from the jaywalker when the jaywalker finishes crossing the street is then X - x.
Without the values of T and a, we can't complete the calculations. But this is the step-by-step process to solve the problem.
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