Time elapsed between seeing a crash and hearing the crash

[danshodan]

Homework Statement

A race car fan is sitting in the first row at the beginning of a 1.5 km front stretch of a racetrack. A race car driver coming around the final turn is approaching the fan’s position at 99.5 m/s. The driver sees a car wreck ahead and slams on the brakes causing the car to slow at 4.7 m/s2. Unfortunately, the driver crashes into the wreck at 27.3 m/s. If the speed of sound in the air is 343 m/s, how much time elapses from the moment the fan sees the crash and when the fan hears the crash?

Homework Equations

v=fλ
d=vt

The Attempt at a Solution

using the info:
v1= 99.5 m/sec v2=27.3 m/sec
i tried to use d=vt to find the t(ime) but i couldn't figure out d.
Eventually i got that t=1.53 by using v2=vi+at and d=vit+0.5at^2, but the correct answer should be 2.8s? I don't know how to get there

 

[mukundpa]

Find the distance at which the crash took place from the fan. Time taken by the sound to cover this distance will be the difference( neglecting the time taken by the light comparatively.

 

[m2003]

I would approach this problem by first understanding the concept of speed of sound and how it relates to the distance between the fan and the crash. The speed of sound is the rate at which sound waves travel through a medium, in this case, the air. The distance between the fan and the crash is 1.5 km, which is equal to 1500 m.

Next, I would use the formula v=d/t to calculate the time it takes for the sound of the crash to reach the fan. We know that the speed of sound is 343 m/s, so we can plug in this value for v and 1500 m for d.

343 m/s = 1500 m / t

Solving for t, we get t = 1500 m / 343 m/s = 4.38 seconds.

However, this only gives us the time it takes for the sound to travel from the crash to the fan. We also need to consider the time it takes for the fan to see the crash. Since the fan is sitting in the first row, we can assume that the distance between the fan and the crash is negligible. Therefore, we can use the same formula to calculate the time it takes for light to travel from the crash to the fan.

The speed of light is much faster than the speed of sound, so we can approximate it to be instantaneous. This means that the time it takes for the fan to see the crash is also 4.38 seconds.

Therefore, the total time elapsed between seeing the crash and hearing the crash is 4.38 seconds + 4.38 seconds = 8.76 seconds.

In conclusion, as a scientist, I would use the concept of speed of sound and the distance between the fan and the crash to calculate the time it takes for the sound to reach the fan. I would also consider the speed of light and the negligible distance between the fan and the crash to calculate the time it takes for the fan to see the crash. By adding these two times together, I would arrive at the total time elapsed between seeing the crash and hearing the crash.