A boat is travelling at 8.9km/h relative to the water in the river.The boat aims straight for the opposite bank of the river which is 120.9m wide,if the speed of water in the river is 2.9km/h.how far down stream will the boat be when it reaches the opposite side
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First stage I to determine the time that the boat will use to move to other opposite bank,then after getting the time the next step is find the distance that a boat will move to other river bank
I need assistance to that question above
To find how far downstream the boat will be when it reaches the opposite side of the river, we need to determine the boat's actual velocity.
The boat's velocity can be broken into two components: its velocity relative to the water and the velocity of the water itself.
Let's start by converting the boat's velocity and the velocity of the water from kilometers per hour (km/h) to meters per second (m/s) to ensure consistent units.
Boat's velocity relative to the water = 8.9 km/h = 8.9 * (1000/3600) m/s ≈ 2.472 m/s
Velocity of the water = 2.9 km/h = 2.9 * (1000/3600) m/s ≈ 0.806 m/s
Now, since the boat is crossing the river and aiming straight for the opposite bank, we can treat it as a right-angled triangle. The boat's velocity relative to the ground will be the hypotenuse, and the downstream component will be the base of the triangle.
Using the Pythagorean theorem, we can find the boat's velocity relative to the ground:
Velocity relative to the ground = √(velocity of the water)^2 + (velocity of the boat relative to the water)^2
= √(0.806^2 + 2.472^2) m/s
≈ √(0.649 + 6.095) m/s
≈ √6.744 m/s
≈ 2.599 m/s
Now, we can calculate the time it takes for the boat to cross the river:
Time = distance / velocity relative to the ground
= 120.9 m / (2.599 m/s)
≈ 46.53 seconds
Finally, we can determine how far downstream (distance along the river) the boat will be when it reaches the opposite side. This can be found by multiplying the time taken to cross the river by the velocity of the water:
Distance downstream = velocity of the water * time
= 0.806 m/s * 46.53 s
≈ 37.56 meters
Therefore, when the boat reaches the opposite side, it will be approximately 37.56 meters downstream.
To find the distance down stream that the boat will be when it reaches the opposite side, we need to break the boat's velocity into two components: horizontal and vertical.
The horizontal component of the boat's velocity is its speed relative to the water, which is 8.9 km/h. The vertical component of the boat's velocity is the speed of the river current, which is 2.9 km/h.
Since the boat aims straight for the opposite bank, the horizontal component will determine the time it takes for the boat to cross the river. We can use the formula:
time = distance / velocity
The distance is the width of the river, which is 120.9 m (converted to km: 120.9/1000 = 0.1209 km)
The velocity is the boat's speed relative to the water, which is 8.9 km/h.
time = 0.1209 km / 8.9 km/h
time = 0.0136 hours
Now that we know the time, we can calculate the distance downstream that the boat will be:
distance downstream = vertical component of velocity * time
The vertical component of velocity is the speed of the river current, which is 2.9 km/h.
distance downstream = 2.9 km/h * 0.0136 hours
distance downstream = 0.0394 km
Therefore, the boat will be approximately 0.0394 km (or 39.4 m) downstream when it reaches the opposite side.
Well, that depends on how well the boat can parallel park in the river! Just kidding. Let's do some math.
To find out how far downstream the boat will be, we need to consider the velocity of the boat and the velocity of the river.
The boat is traveling at 8.9 km/h relative to the water, and the river is flowing at 2.9 km/h. So, the combined velocity of the boat and the river is 8.9 + 2.9 = 11.8 km/h.
Now, we know that the boat needs to travel across a river that is 120.9 meters wide.
To figure out the time it takes for the boat to cross, we need to convert the width of the river into the same units as the velocity. So, 120.9 meters = 0.1209 kilometers.
Next, we use the formula: time = distance / velocity.
Therefore, the time it takes for the boat to cross is: 0.1209 km / 11.8 km/h = 0.0103 hours.
Now, we can find out how far downstream the boat will be by multiplying the time it takes to cross by the downstream velocity, which is the river's velocity: 0.0103 hours * 2.9 km/h = 0.02987 km.
Converting this back to meters, we get: 0.02987 km * 1000 m/km = 29.87 meters.
So, the boat will end up approximately 29.87 meters downstream when it reaches the opposite side of the river.
Hope that helps, and remember, the river might try to take the boat on a joyride, but it can't beat a determined captain!