Answer:
t = 4.468 h
Explanation:
For this exercise let's start by calculating the distance where the boat is
the first trip is 50 miles at 45 °, then 90 miles at 80 °,
to find the total distance let's find the distance of each displacement
cos 45 = x₁ / 50
sin 45 = y₁ / 50
x₁ = 50 cos 45 = 35.35 miles
y₁ = 50 cos 45 = 35.35 miles
cos 80 = x₂ / 90
sin 80 = y₂ / 90
x₂ = 90 cos 80 = 15.63 miles
y₂ = 90 sin 80 = 88.63 miles
let's find the total displacement in each axis
x_total = x₁ + x₂
x_total = 35.35 + 15.63
x_total = 50.98 miles
y_total = y₁ + y₂
y_total = 35.35 + 88.63
y_total = 123.98 miles
Let's use the Pythagorean theorem to find the modulus of the displacement
R = √ (x_total² + y_total²)
R = √ (50.98² + 123.98²)
R = 134.05 miles
The boat goes at a constant speed,
v = R / t
t = R / v
let's calculate
t = 134.05 / 30
t = 4.468 h
