Question

A motorboat traveling 4 m/s, East encounters a current traveling 3 m/s, South.What is the resultant velocity of the motor boat

Answer 1

Ответ:

сенде физика онлайн мектеп барма тжб

Answer 2

To find the resultant velocity of the motorboat, you can use vector addition because the boat's velocity and the current's velocity are in different directions. You can use the Pythagorean theorem to find the magnitude of the resultant velocity, and trigonometry to find its direction.

Let's break it down step by step:

1. The motorboat's velocity is 4 m/s to the east. We'll call this velocity "Vb" (for boat): Vb = 4 m/s east

2. The current's velocity is 3 m/s to the south. We'll call this velocity "Vc" (for current): Vc = 3 m/s south

3. Now, we need to find the resultant velocity "Vr" of the motorboat. To do this, we'll treat the boat's velocity and the current's velocity as perpendicular components of a right triangle, and we'll use the Pythagorean theorem to find the magnitude of Vr:

   Vr = √(Vb^2 + Vc^2)

   Vr = √((4 m/s)^2 + (3 m/s)^2)

   Vr = √(16 m^2/s^2 + 9 m^2/s^2)

   Vr = √(25 m^2/s^2)

   Vr = 5 m/s

So, the magnitude of the resultant velocity of the motorboat is 5 m/s.

4. To find the direction of the resultant velocity, we can use trigonometry. The boat's velocity (4 m/s east) and the current's velocity (3 m/s south) form a right triangle, and we want to find the angle θ between the resultant velocity vector and the east direction. We can use the tangent function:

   tan(θ) = (Vc / Vb)

   tan(θ) = (3 m/s) / (4 m/s)

   θ = arctan(3/4)

   θ ≈ 36.87 degrees

So, the direction of the resultant velocity of the motorboat is approximately 36.87 degrees south of east.