A truck travels 1710 m uphill along a road that makes a constant angle of 5 . 08 ◦ with the horizontal. Find the magnitude of the truck’s horizontal component of displacement. Answer in units of m.

Dx = 1710*Cos5.08 =

To find the magnitude of the truck's horizontal component of displacement, we can use trigonometry.

The horizontal component of displacement can be found by using the cosine function.

cos(angle) = adjacent/hypotenuse

In this case, the horizontal component of displacement is the adjacent side, and the hypotenuse is the total displacement of the truck.

Given that the total displacement is 1710 m and the angle is 5.08°, we can plug the values into the formula:

cos(5.08°) = adjacent/1710 m

To isolate the adjacent side, we rearrange the formula:

adjacent = cos(5.08°) * 1710 m

Using a scientific calculator or the cosine function on a calculator, we find:

cos(5.08°) ≈ 0.99663

Substituting this value into the formula:

adjacent = 0.99663 * 1710 m

Calculating this expression, we find:

adjacent ≈ 1705.67 m

Therefore, the magnitude of the truck's horizontal component of displacement is approximately 1705.67 m.

To find the magnitude of the truck's horizontal component of displacement, we need to use trigonometry. We can use the angle of incline and the distance traveled uphill to determine the horizontal displacement.

Let's call the horizontal component of displacement "x." Since the angle of incline is given as 5.08 degrees, we can use the trigonometric function cosine to relate the horizontal displacement to the total displacement.

The equation we can use is:

cos(angle) = adjacent / hypotenuse

In this case, the hypotenuse is the total displacement traveled uphill, which is given as 1710m. The adjacent side is the horizontal component of displacement, which is what we want to find.

Plugging in the values into the equation, we have:

cos(5.08 degrees) = x / 1710m

Now, we can solve for x:

x = cos(5.08 degrees) * 1710m

Calculating this, we get:

x ≈ 1703.42m

Therefore, the magnitude of the truck's horizontal component of displacement is approximately 1703.42m.

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