a boat leaves a dock at 2:00 pm and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 3:00 pm. at what time were the two boats closest together

make a diagram.

It took the eastbound ship 1 hr to reach the dock, so when the southbound ship was at the dock, the eastbound ship was 15 km from the dock

So after t hrs, the southbound ship went 20t
and the eastbound ship went 15t
I see a right-angled triangle with a vertical of 20t and a horizontal of 15-15t
let d be the distance between them
d^2 = (20t)^2 + (15-15t)^2
2d dd/dt = 2(20t)(20) + 2(15-15t)(-15)
at a minimum of d, dd/dt = 0
800t - 30(15-15t) = 0
800t - 450 + 450t = 0
1250t = 450
t = .36 hrs or 21.6 minutes
so they were closest at 2:21:36 pm

check:
when t = .36 , d^2 = 51.84 + 92.16 = 144, d = 12
take a value slightly higher and smaller
t = .37 , d^2 = 54.76 + 89.3025 = 144.0625 , d = 12.0026 , slightly farther
t = .35 , d^2 = 49 + 95.0625 = 144.0625 , d = 12.0026 , again slightly farther

my answer is correct

To determine the time when the two boats were closest together, we need to find the point of intersection between their paths. Since one boat is traveling due south and the other is traveling due east, the point of intersection will occur when the distances traveled by both boats are equal.

Let's break down the problem step by step:

1. Define variables: Let's use t as the time in hours after 2:00 pm when the boats were closest together.

2. Calculate the distance traveled by each boat at time t:
- For the boat traveling due south: Since its speed is 20 km/h, the distance it traveled would be 20 * t km.
- For the boat traveling due east: The time it took to reach the dock is given as 3:00 pm, which is 1 hour. Hence, the distance it traveled would be 15 km/h * 1 h = 15 km.

3. Set up an equation and solve for t:
Since the distances traveled by both boats are equal at the point of intersection, we can set up the equation:
20t = 15
Solve this equation to find the value of t.

20t = 15
t = 15 / 20
t = 0.75 hours

4. Convert the time in hours to minutes:
Since we started at 2:00 pm, we need to convert 0.75 hours to minutes:

0.75 hours * 60 minutes/hour = 45 minutes

The two boats were closest together at 2:00 pm + 45 minutes, which is 2:45 pm.

The answer is 14 protons.

(-5)|36|

first, find the integral and divide by the derivative. Then, find the time component of the acceleration vector on the complex plane.