My problem:
One runner in a relay race has a 1.50 s lead and is running at a constant speed of 3.25 m/s. The runner has 30.0 m to run before reaching the end of the track. A second runner moves in the same direction as the leader. What constant speed must the second runner maintain in order to catch up to the leader at the end of the race?
My answer:
4.75 m/s
Please help! I will really appreciate it. :)
Never mind. I figured the answer out. It was 3.9 m/s.
no
A fish swims 12.0 m in 5.0 s. It swims the first 4.0 m in 2.0 s, the next 3.0 m in 1.2 s, and the last 5.0 m in 1.8 s. What is the average velocity of the fish during the time interval between 0.0 s and 3.2 s?
To solve this problem, we can set up an equation based on the information given.
Let's assume the time it takes for the second runner to catch up to the leader is t seconds.
For the first runner:
Distance = Speed × Time
Distance = 3.25 m/s × t seconds
For the second runner:
Distance = Speed × Time
Distance = Speed × (t + 1.50) seconds
Since both runners reach the end of the track at the same time, their distances covered must be equal:
3.25t = Speed × (t + 1.50)
Now, we can solve this equation for the speed of the second runner:
3.25t = Speed × t + 1.50Speed
To isolate the Speed term, we can rearrange the equation:
3.25t - tSpeed = 1.50Speed
Combining like terms:
3.25t = (1.50 + t)Speed
Now divide both sides by (1.50 + t):
Speed = (3.25t) / (1.50 + t)
Substituting the given values into the equation:
Speed = (3.25 × 30.0) / (1.50 + 30.0)
Speed = 97.5 / 31.5
Speed ≈ 3.095 m/s
Therefore, the second runner must maintain a constant speed of approximately 3.095 m/s in order to catch up to the leader at the end of the race.
It looks like the answer you provided, 4.75 m/s, is not correct. Double-check the calculations to ensure accuracy.