An army tank division leaves base and travels 30 miles at 30° S of W and then turns and travels 70 miles at 10° N of W. What is their total displacement from base at the end of the trip?
the answer i got is 94.96,
what did you get?
30 at W30°S takes them (-25.98,-15.00)
70 at W10°N takes them (-98.48,+17.36)
add them to get (-124.46,2.36)
That's 124.48 at W1.08°N
since we disagree, better check my math.
this is what you got: 70 at W10°N takes them (-98.48,+17.36)
but on a coordinate grid system, wouldn't 10 degrees N of W mean 170 degrees?
so shouldn't the second part be <70 cos 170, 70 sin 170>
the first part is the same, but the second part is different, so im not sure who's right
To find the total displacement from the base, we need to use vector addition. We can break down the displacement into its horizontal and vertical components.
Let's start with the first leg of the trip: traveling 30 miles at 30° S of W. We can find the horizontal and vertical components of this displacement using trigonometry.
The horizontal component can be calculated by multiplying the magnitude of the displacement (30 miles) by the cosine of the angle (30°):
Horizontal component = 30 miles * cos(30°) ≈ 26.0 miles
The vertical component can be calculated by multiplying the magnitude of the displacement (30 miles) by the sine of the angle (30°), but since it is South, it will be negative:
Vertical component = -30 miles * sin(30°) ≈ -15.0 miles
Now, let's move on to the second leg of the trip: traveling 70 miles at 10° N of W. We can again find the horizontal and vertical components using trigonometry.
The horizontal component can be calculated by multiplying the magnitude of the displacement (70 miles) by the cosine of the angle (10°):
Horizontal component = 70 miles * cos(10°) ≈ 68.15 miles
The vertical component can be calculated by multiplying the magnitude of the displacement (70 miles) by the sine of the angle (10°):
Vertical component = 70 miles * sin(10°) ≈ 12.17 miles
Now, we can add up the horizontal and vertical components to get the total displacement:
Total horizontal displacement = 26.0 miles + 68.15 miles ≈ 94.15 miles
Total vertical displacement = -15.0 miles + 12.17 miles ≈ -2.83 miles
Total displacement = √((Total horizontal displacement)² + (Total vertical displacement)²)
≈ √(94.15 miles)² + (-2.83 miles)²
≈ √(8845.57 miles + 8.01 miles)
≈ √8853.58 miles
≈ 94.02 miles
So, the total displacement from the base at the end of the trip is approximately 94.02 miles.
It seems like you got an answer of 94.96 miles. Please double-check your calculations to verify if there was an error made during the calculation.