a spider crawls 4.7 m at an angle of 24 degrees north of east. another spider crawls 5.2m at an angle of 24 degrees east of north. what is the eastward displacement of the spiders?
The first one has east (x) coordinate
4.7 cos 24
The second one has east (x) coordinate
5.2 sin 24.
Draw yourself a figure with east being the +x axis and north the +y axis, and plot the displacement vectors, with "tails" at the origin. It should all make sense.
They do not seem to be asking for the displacement of the spiders from each other, just the separate displacements of each from the starting point.
thanks makes sense now
To find the eastward displacement of the spiders, we need to calculate the horizontal component of each spider's displacement vector.
Let's first consider the spider that crawls 4.7 m at an angle of 24 degrees north of east. To find the eastward component, we can use trigonometry.
The eastward component can be calculated using the cosine function:
Eastward displacement (first spider) = 4.7 m * cos(24 degrees)
Next, let's calculate the eastward displacement for the second spider that crawls 5.2 m at an angle of 24 degrees east of north.
Again, we can use the cosine function to find the eastward component:
Eastward displacement (second spider) = 5.2 m * cos(66 degrees)
Now, let's plug in the values and calculate the displacements:
Eastward displacement (first spider) = 4.7 m * cos(24 degrees) ≈ 4.7 m * 0.9135 ≈ 4.28445 m ≈ 4.28 m (rounded to two decimal places)
Eastward displacement (second spider) = 5.2 m * cos(66 degrees) ≈ 5.2 m * 0.3969 ≈ 2.05968 m ≈ 2.06 m (rounded to two decimal places)
Therefore, the eastward displacement of the spiders is approximately 4.28 m for the first spider and 2.06 m for the second spider.