A ship leaves the island of Guam and sails a distance 295 at an angle 35.0 north of west.
How far must it sail so that its resultant displacement will be 100 directly east of Guam?
You need some units for distance.
100E= 295@35 NofW+ Far
100E=295cos35 W + 295sin35N + howfar
so how far= East(100+295cos35)+South(295sin35)
the unit of the distance is km but plz can you give me the answer directly
A ship leaves the island of Guam and sails a distance 300 at an angle 41.0 north of west.
To find the distance the ship must sail, we need to calculate the magnitude of the resultant displacement vector that will be 100 miles directly east of Guam.
Given:
Magnitude of the initial displacement vector (d1) = 295 miles
Angle between the initial displacement vector and the west direction (θ1) = 35.0°
To solve the problem, we can break down the initial displacement vector into its horizontal (x) and vertical (y) components using trigonometry. Then we can add the eastward displacement to the x-component to find the resultant displacement vector.
Step 1: Find the x-component of the initial displacement vector.
Using cosine function:
x = d1 * cos(θ1)
x = 295 miles * cos(35.0°)
Step 2: Find the eastward displacement required to be added to the x-component, which will result in a displacement of 100 miles directly east of Guam.
Let's call this eastward displacement as dx.
x + dx = 100 miles
Step 3: Solve for dx using the equation from Step 2.
dx = 100 miles - x
Step 4: Calculate the magnitude of the resultant displacement vector using the Pythagorean theorem.
Resultant displacement vector (d2) = sqrt(dx^2 + d1^2)
d2 = sqrt( (100 miles - x)^2 + (295 miles)^2 )
Now let's substitute the value of x from Step 1 and calculate d2.
x ≈ 224.695 miles
d2 = sqrt( (100 miles - 224.695 miles)^2 + (295 miles)^2 )
d2 ≈ 399.176 miles
Therefore, the ship must sail approximately 399.176 miles so that its resultant displacement will be 100 miles directly east of Guam.