Two professional downhill skiers are racing at the speeds shown in the diagram. *Skier 1 is going 100 ft/s, and Skier 2 is going 110 ft/s. Skier 1 starts 5 seconds before Skier 2. The course is 5000 ft long. Will Skier 2 pass Skier 1?
5000/100 = 50
5000/110 = 45.45
so, since skier 1 started 5 seconds early, he will finish 0.55 seconds ahead
Thank you!
Can I ask why you divided the course length by the speeds?
To determine if Skier 2 will pass Skier 1, we need to compare the distances covered by both skiers over a given interval of time.
First, let's calculate the time it takes for Skier 1 to reach the end of the course, which is 5000 ft long. Using the formula distance = speed * time, we can plug in the given values:
distance = speed * time
5000 ft = 100 ft/s * t1
Solving for t1, we divide both sides by 100 ft/s:
t1 = 5000 ft / 100 ft/s = 50 seconds
Now, let's calculate the time it takes for Skier 2 to reach the end of the course. Since Skier 2 starts 5 seconds after Skier 1, we need to subtract that time from the total time for Skier 2:
t2 = t1 - 5 seconds = 50 seconds - 5 seconds = 45 seconds
Next, let's calculate the distance covered by Skier 2 when he catches up with Skier 1. Since both skiers travel at a constant speed, we can use the formula distance = speed * time:
distance_skier2 = speed_skier2 * t2
distance_skier2 = 110 ft/s * 45 seconds
distance_skier2 = 4950 ft
So, when Skier 2 catches up with Skier 1, he will have covered a distance of 4950 ft. Since the entire course is 5000 ft, it means that Skier 2 will not completely pass Skier 1. Skier 2 will be 50 ft behind Skier 1 when they both reach the end of the course.
Therefore, Skier 2 will not pass Skier 1.