A race car is one lap behind the lead race car when the lead car has 57 laps to go in a race. If the speed of the lead car is 66.2 m/s, what must be the average speed of the second car to catch the lead car just before the end of the race (i.e., right at the finish line)? Assume 1 lap is 1.34 km.
Answer in units of m/s
How long before the lead car finishes?
57 * 1.34 = 76.38 km = 76.38*10^3 m
t = distance/speed = 76.38*10^3/66.2 = 1157 seconds
So in 1157 seconds second car must go
58 * 1.34 = 77.72 km = 77.72*10^3 m
speed = distance/time = 77.72/1.157 = 67.2 m/s
Never mind I figured it out the answer is 67.3614 if anyone needs help
Why did the race car bring a ladder to the track? Because it wanted to climb the leaderboard! Now, let's calculate the average speed of the second car and help it chase down the lead car.
First, we need to determine the distance the second car needs to catch up. Since the lead car has 57 laps to go, it means it has covered 57 laps + 1 lap behind = 58 laps in total. Each lap is 1.34 km, so the lead car has traveled 58 laps * 1.34 km/lap = 77.72 km.
To catch up just before the finish line, the second car needs to cover the same distance, 77.72 km. But we need the answer in m/s, so let's convert it first. 1 km equals 1000 m, so 77.72 km = 77.72 km * 1000 m/km = 77,720 m.
Now, we divide the distance by the time it takes for the second car to catch up to find the average speed. However, we don't have the time given, so we need to find it.
Since the second car is one lap behind the lead car, it means it has to cover a distance of 1 lap * 1.34 km = 1.34 km.
To convert it into meters, we multiply it by 1000: 1.34 km * 1000 m/km = 1340 m.
Now, we can calculate the time using the formula: time = distance / speed.
Time = 1340 m / speed of the second car.
Since we want the second car to catch up at the finish line, we know that the time it took is the same as the time remaining for the lead car, which is 57 laps * 1 lap / 66.2 m/s = 0.8612 s.
So, 0.8612 s = 1340 m / speed of the second car.
To find the speed of the second car, we rearrange the equation: speed of the second car = 1340 m / 0.8612 s.
Calculating this gives us a speed of approximately 1557.3 m/s.
Therefore, the average speed of the second car must be approximately 1557.3 m/s to catch the lead car just before the finish line.
To answer this question, we can use the concept of relative speed. Let's break down the problem step by step:
1. First, let's calculate the total distance that the lead car needs to cover until the finish line. We know that 1 lap is 1.34 km, and the lead car has 57 laps to go. Thus, the total distance is 1.34 km/lap * 57 laps = 76.38 km.
2. Next, we need to determine the time it takes for the lead car to cover this distance. We can use the formula time = distance/speed. Therefore, the time taken by the lead car to cover the distance is 76.38 km / 66.2 m/s = 1155.8 seconds.
3. Now, we need to find the speed at which the second car needs to travel in order to catch up with the lead car just before the finish line. Since the second car is one lap behind, it needs to cover the same distance as the lead car (76.38 km) in the remaining time (1155.8 seconds).
4. As we have the time and distance, we can find the average speed of the second car using the formula speed = distance/time. Thus, the average speed of the second car should be 76.38 km / 1155.8 seconds = 0.0661 km/s.
5. Finally, we need to convert the speed to meters per second (m/s) since the answer should be in those units. Since 1 km = 1000 m, we can convert the average speed of the second car from km/s to m/s by multiplying it by 1000. Therefore, the average speed of the second car should be 0.0661 km/s * 1000 = 66.1 m/s.
So, the average speed of the second car must be 66.1 m/s in order to catch the lead car just before the end of the race.