A boat travels at 8m/sec and heads straight across a river 240m wide. The river flows at 4m/sec. What is the boats resultant speed with respect to the riverbank
To find the boat's resultant speed with respect to the riverbank, we need to use vector addition. The boat's velocity consists of two components: its velocity directly across the river (perpendicular to the river's flow) and its velocity due to the river's flow (parallel to the river's flow).
First, let's find the boat's velocity directly across the river. Since the boat is traveling at a speed of 8 m/sec and the width of the river is 240 m, it will take the boat 240 m / 8 m/sec = 30 seconds to cross the river.
Next, let's find the boat's velocity due to the river's flow. The river is flowing at a speed of 4 m/sec. Since the boat is traveling perpendicular to the river's flow, the river's current does not affect the boat's speed directly across the river. Therefore, the boat's velocity due to the river's flow is 4 m/sec.
To find the resultant velocity of the boat, we need to use vector addition. Since the velocity directly across the river and the velocity due to the river's flow are perpendicular to each other, we can use the Pythagorean theorem.
Resultant velocity = √(velocity directly across the river)^2 + (velocity due to the river's flow)^2
Plugging in the values, we get:
Resultant velocity = √(8 m/sec)^2 + (4 m/sec)^2
= √(64 m^2/sec^2) + (16 m^2/sec^2)
= √(80 m^2/sec^2)
≈ 8.94 m/sec (rounded to two decimal places)
Therefore, the boat's resultant speed with respect to the riverbank is approximately 8.94 m/sec.
To find the resultant speed of the boat with respect to the riverbank, we can use the concept of vector addition.
Let's break down the velocities into their horizontal and vertical components.
The boat's velocity consists of two components:
1. The horizontal component, which is the velocity at which the boat travels across the river.
2. The vertical component, which is the velocity due to the river's flow.
The boat's horizontal component remains constant at 8 m/sec because it is traveling straight across the river.
The boat's vertical component is the river's flow, which is 4 m/sec.
Now we can calculate the boat's resultant velocity using the Pythagorean theorem, which relates the lengths of the sides of a right triangle:
Resultant velocity^2 = Horizontal velocity^2 + Vertical velocity^2
Resultant velocity^2 = (8 m/sec)^2 + (4 m/sec)^2
Resultant velocity^2 = 64 m^2/sec^2 + 16 m^2/sec^2
Resultant velocity^2 = 80 m^2/sec^2
Taking the square root of both sides, we get:
Resultant velocity = sqrt(80 m^2/sec^2)
Resultant velocity ≈ 8.94 m/sec
Therefore, the boat's resultant speed with respect to the riverbank is approximately 8.94 m/sec.