a motorboat is driven across a river at 5km/h at right angles to a current flowing at 3.9km/h. What is the resulting speed of the motorboat?
When you add the two perpendicular vectors, the resultant vector will be the hypotenuse.
sqrt[(5^2) + (3.9)^2] = ___
6.34km/h
To find the resulting speed of the motorboat, we can use the concept of vector addition.
Let's call the speed of the motorboat across the river V_boat, and the speed of the current V_current.
The motorboat is traveling at 5 km/h at right angles to the current. This means that the actual speed of the motorboat is the hypotenuse of a right triangle formed by the boat's speed and the current's speed. We can use the Pythagorean theorem to find the resulting speed:
resulting speed^2 = (speed across the river)^2 + (speed of the current)^2
resulting speed^2 = (5 km/h)^2 + (3.9 km/h)^2
resulting speed^2 = 25 km^2/h^2 + 15.21 km^2/h^2
resulting speed^2 = 40.21 km^2/h^2
Taking the square root of both sides, we get:
resulting speed = sqrt(40.21 km^2/h^2)
resulting speed ≈ 6.34 km/h
Therefore, the resulting speed of the motorboat is approximately 6.34 km/h.
To find the resulting speed of the motorboat, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the motorboat's speed across the river is one side, and the current's speed is the other side. The resulting speed of the motorboat is the hypotenuse.
Let's break the problem down into the given values:
Speed across the river (one side of the triangle) = 5 km/h
Speed of the current (the other side of the triangle) = 3.9 km/h
To find the resulting speed, we can use the formula:
Resulting speed^2 = (Speed across the river)^2 + (Speed of the current)^2
Plugging in the values:
Resulting speed^2 = (5 km/h)^2 + (3.9 km/h)^2
Resulting speed^2 = 25 km²/h² + 15.21 km²/h²
Resulting speed^2 = 40.21 km²/h²
To find the resulting speed, we need to take the square root of both sides:
Resulting speed = √(40.21 km²/h²)
Resulting speed ≈ 6.34 km/h
Therefore, the resulting speed of the motorboat is approximately 6.34 km/h.