A ferry is crossing a river. If the ferry is headed due north with a speed of 3.2 m/s relative to the water and the river's velocity is 4.3 m/s to the east, What will the ferry's velocity relative to the shore be?
(Choose the nearest answer)
0.58 m/s , 12degree
28.4 m/s , 56.5degree
5.36 m/s , 36.6degree
3 4 5 triangle so about 5
Oh come on ! Look at your choices !!!!
To determine the ferry's velocity relative to the shore, we can use vector addition. The ferry's velocity consists of its velocity relative to the water (3.2 m/s north) and the river's velocity (4.3 m/s east).
To add these velocities, we can use the Pythagorean theorem to find the magnitude of the resulting velocity:
V^2 = (Vx)^2 + (Vy)^2
Where V is the resultant velocity, Vx is the velocity in the horizontal direction (east), and Vy is the velocity in the vertical direction (north).
Vx = 4.3 m/s (east)
Vy = 3.2 m/s (north)
Substituting the values:
V^2 = (4.3)^2 + (3.2)^2
V^2 = 18.49 + 10.24
V^2 = 28.73
To find the magnitude of the velocity, we take the square root of both sides:
V ≈ √28.73
V ≈ 5.36 m/s (rounded to the nearest answer option)
Next, we need to find the angle (θ) between the resultant velocity (V) and the east direction. We can use trigonometry to determine this:
θ = tan^(-1) (Vy/Vx)
θ = tan^(-1) (3.2/4.3)
θ ≈ 36.6 degrees (rounded to the nearest answer option)
Therefore, the ferry's velocity relative to the shore will be approximately 5.36 m/s at an angle of 36.6 degrees, which corresponds to option "5.36 m/s, 36.6 degrees."