Answer:
R = 3,936 km θ=105º
Step-by-step explanation:
This is a problem of vector addition, let's find it takes time for the ship to reach the ocean
v1 = x1 / t1
t1 = 2.50 / 3.80
t1 = 0.658 h
Let's analyze how much travel time is left
t2 = 1 h - t1
t2 = 1 - 0.658
t2 = 0.342 h
This is the time he walked by the ocean, let's calculate every distance he traveled
X axis
v2 = -3.00 km / h
x = v t
x2 = -3.00 * 0.342
x2 = - 1,026 km
Axis y
v1 = 3.80 km / h
y2 = v1 t2
y2 = 3.80 0.342
y2 = 1.30 km
The total distance on each axis is
xall = x2
xall = -1,026 km
y all = 2.5 + y2
y all = 2.5 + 1.3
y all = 3.8 km
Let's calculate the distance and angle from the pier with the Pythagorean theorem and trigonometry
R² = xall² + yall²
R = √(1,026² + 3.8²)
R = 3,936 km
tan θ = yall / xall
tan θ = 3.8 / 1.026
θ = tan -1 (3.70)
θ = 75º
The angle measured from the x axis (East) is 180 - 74 = 105º