Uniform Motion Related Problem
Port A is 25 km downriver from port B. At noon a tugboat leaves port B and travels upstream at 15 kph. At 3 p.m. a hyrodrofoil leaves Port A travelling upstream at 50 kph. At what time will the hydrofoil pass the tugboat?
by 3:00, the tug has traveled upstream 3*15 = 45 km, so it is now 20 km upstream from B.
The boats' relative speed is 35 km/hr, so how long does it take the foil to make up the 20 km head start of the tug?
Add that time to 3:00.
To solve this uniform motion problem, we can use a concept known as relative velocity.
First, let's establish the following variables:
- Distance between port A and port B: 25 km
- Speed of the tugboat: 15 kph
- Speed of the hydrofoil: 50 kph
Since the tugboat starts from port B, we can calculate the time it takes for it to reach the point of intersection with the hydrofoil. Let's call this time "t".
The hydrofoil starts from port A at 3 p.m., which means it has a head start of 3 hours (since noon). Therefore, by the time the tugboat reaches the point of intersection, the hydrofoil has been traveling for t + 3 hours.
Now let's calculate the distance traveled by each:
Distance covered by the tugboat (d1) = Speed of the tugboat (15 kph) × Time taken by the tugboat (t)
Distance covered by the hydrofoil (d2) = Speed of the hydrofoil (50 kph) × Time taken by the hydrofoil (t + 3)
Since both the tugboat and the hydrofoil meet at the same point, the distance traveled by each should be the same:
d1 = d2
Using the obtained expressions for d1 and d2, we can set up an equation:
15t = 50(t + 3)
Now, let's solve for t:
15t = 50t + 150
Subtracting 50t from both sides:
15t - 50t = 150
-35t = 150
Dividing both sides by -35:
t = -150 / -35
t ≈ 4.29 hours
Therefore, it takes approximately 4.29 hours for the tugboat and hydrofoil to meet after the tugboat leaves port B.
To determine the time of their meeting, we can add this time to the time the hydrofoil started (3 p.m.):
Time of meeting = Starting time of the hydrofoil (3 p.m.) + Time taken by the tugboat (4.29 hours)
Time of meeting ≈ 3 p.m. + 4.29 hours
Time of meeting ≈ 7:17 p.m.
So, the hydrofoil will pass the tugboat at approximately 7:17 p.m.