A man paddles a canoe at 6.0 km per hour. If he paddles on a river with a current of 6.0 km per hour, ? What is the speed of the canoe if it heads:
a.) Upstream?
b.) Directly across the river?
(a) 6 - 6 = 0
(b) √(6^2+6^2) = 6√2
To find the speed of the canoe in different scenarios, we need to consider the concept of vector addition. The speed of the canoe will be affected by the speed and direction of the river's current.
a.) Upstream:
When paddling upstream, the canoe moves against the current. To determine the speed, we subtract the speed of the current from the speed of the canoe.
Speed of canoe upstream = Speed of canoe - Speed of current
In this case, the speed of the canoe is 6.0 km/h, and the speed of the current is also 6.0 km/h.
Speed of canoe upstream = 6.0 km/h - 6.0 km/h
Speed of canoe upstream = 0 km/h
Therefore, the speed of the canoe upstream is 0 km/h since it is unable to move against the current.
b.) Directly across the river:
When paddling directly across the river, the current does not affect the speed of the canoe. The speed of the canoe remains the same.
Speed of canoe across the river = Speed of canoe
In this case, the speed of the canoe is still 6.0 km/h.
Therefore, the speed of the canoe when it paddles directly across the river is 6.0 km/h.
To find the speed of the canoe when paddling upstream and when paddling directly across the river, we need to consider the effect of the current on the canoe's speed.
a.) Upstream:
When the canoe paddles upstream, it is moving against the current. In this case, the speed of the canoe relative to the ground will be the difference between the speed of the canoe and the speed of the current. So, to find the speed of the canoe paddling upstream, we subtract the speed of the current from the speed of the canoe.
Speed of the canoe upstream = Speed of the canoe - Speed of the current
Given that the speed of the canoe is 6.0 km/h and the speed of the current is also 6.0 km/h, we can substitute the values into the formula:
Speed of the canoe upstream = 6.0 km/h - 6.0 km/h = 0 km/h
b.) Directly across the river:
When the canoe paddles directly across the river, it is perpendicular to the current. In this case, the speed of the canoe relative to the ground will be the vector sum of the speed of the canoe and the speed of the current. We can use the Pythagorean theorem to calculate the resultant speed.
Speed of the canoe across the river = √((Speed of the canoe)² + (Speed of the current)²)
Substituting the given values:
Speed of the canoe across the river = √((6.0 km/h)² + (6.0 km/h)²)
= √(36 km²/h² + 36 km²/h²)
= √(72 km²/h²)
= √72 km/h
≈ 8.49 km/h
So, the speed of the canoe when paddling upstream is 0 km/h, and when paddling directly across the river is approximately 8.49 km/h.