a boat leaves a dock at 2:00pm ,heading west at 15 km/h. another boat heads south at 12km/hand reaches the same dock at 3:00 pm, when were the boats were closest to each other.? tanks it will be help full if its explained well .
To find out when the two boats are closest to each other, we can start by visualizing their movements on a coordinate grid. Let's assume the dock is located at the origin (0, 0).
The westward boat is traveling at 15 km/h, so after every hour, it will be 15 km further west. We can plot the positions of this boat relative to the dock at different times:
- At 2:00 pm (start time): (-15, 0) [1 hour west of the dock]
- At 3:00 pm (end time): (-30, 0) [2 hours west of the dock]
Similarly, the southbound boat is traveling at 12 km/h, so it will be 12 km further south every hour. We can plot the positions of this boat relative to the dock at different times:
- At 2:00 pm (start time): (0, -12) [1 hour south of the dock]
- At 3:00 pm (end time): (0, -24) [2 hours south of the dock]
Now, we can find the distance between the two boats at each time interval. The distance formula is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
For the start time, the distance between the boats is:
Distance = √((-30 - 0)^2 + (0 - (-12))^2) = √(900 + 144) = √1044 ≈ 32.28 km
For the end time, the distance between the boats is:
Distance = √((-15 - 0)^2 + (0 - (-24))^2) = √(225 + 576) = √801 ≈ 28.31 km
By comparing the distances, we can see that the boats were closest to each other at the end time, which is 3:00 pm.
Therefore, the two boats were closest to each other at 3:00 pm.