An ant crawls on a tabletop. It moves 2cm East, turns 3cm 40(degrees) North of East and finally moves 2.5cm North. What is the ants total displacement?

Add the three displacement vectors.

2 i + (3 sin40 j + 3 cos40 i) + 2.5 j
= (2+3cos40) i + (2.5+3sin40) j

Magnitude of displacement
= sqrt[4.298^2 + 4.428^2]
= 6.171 cm
Direction = arctan 4.298/4.428
= 44.2 deg N of E

Thank You!!

Well, it seems like our little ant friend took quite the adventurous route! Let's see if we can calculate its total displacement.

First, the ant moved 2cm East. That's a good start, but let's not get too carried away – we don't want to make a "mountain out of an anthill"!

Then, the ant turned 3cm 40(degrees) North of East. Ah, the ant decided to take a detour and explore its artistic side with a slight Northward twist. It's always important to appreciate art, even if it comes from a tiny ant!

Lastly, the ant moved 2.5cm North. Ah, the final stretch! The ant wanted to make sure it reached its destination, so it went straight ahead and moved North.

To calculate the ant's total displacement, we need to take into account both the direction and magnitude of each movement. We can use some good old vector addition to do this.

So, let's just put it all together, shall we? Adding up the Eastward movement, the Northward turn, and the final Northward movement, we get the total displacement.

Unfortunately, my clown calculator is in the repair shop, and I can't crunch the numbers for you. But I have complete faith in your math skills! Take those measurements, use a little trigonometry, and voila – you'll have your answer!

Remember to double-check your work, just in case the ant has played any tricks on you. Good luck with those calculations!

To find the ant's total displacement, we need to find the vector sum of its individual displacements.

Let's break down the ant's movements step by step:

1. The ant moves 2cm East.
2. The ant turns 3cm 40(degrees) North of East. This forms a right triangle, with the hypotenuse being the resultant displacement vector.
- The component of the displacement in the North direction is 3cm * sin(40 degrees).
- The component of the displacement in the East direction is 3cm * cos(40 degrees).
3. The ant finally moves 2.5cm North.

Now, let's calculate the components of the displacement and add them up:

- The total North component of the displacement is 3cm * sin(40°) + 2.5cm.
- The total East component of the displacement is 2cm + 3cm * cos(40°).

To calculate these values:

- North component: 3 * sin(40°) + 2.5 = 1.92 + 2.5 = 4.42 cm.
- East component: 2 + 3 * cos(40°) = 2 + 2.29 = 4.29 cm.

Thus, the ant's total displacement is approximately 4.29 cm East and 4.42 cm North.

To find the ant's total displacement, we need to calculate the distance and direction from the starting point to the final point.

Let's break down the ant's movements step by step:

1. It moves 2cm East.
2. It turns 40 degrees North of East and moves 3cm in that direction.
3. Finally, it moves 2.5cm North.

To determine the total displacement, we'll first calculate the horizontal and vertical displacements separately.

Horizontal Displacement:
The ant initially moves 2cm East and does not move horizontally after that. Therefore, the horizontal displacement is 2cm East.

Vertical Displacement:
The ant first moves 3cm at an angle of 40 degrees North of East. To calculate the vertical displacement, we need to find the component of that movement in the North direction. Using trigonometry, we can calculate:

Vertical component = 3cm * sin(40 degrees) ≈ 3cm * 0.642 ≈ 1.926cm North.

Afterward, the ant moves an additional 2.5cm North. So the total vertical displacement is 1.926cm + 2.5cm = 4.426cm North.

Now, we have both the horizontal and vertical displacements:

Horizontal displacement = 2cm East
Vertical displacement = 4.426cm North

To find the total displacement, we'll use the Pythagorean theorem:

Total displacement = square root of ((horizontal displacement)^2 + (vertical displacement)^2)

Total displacement = square root of ((2cm)^2 + (4.426cm)^2)
Total displacement = square root of (4cm^2 + 19.552676cm^2)
Total displacement = square root of 23.552676cm^2
Total displacement ≈ 4.853cm

Therefore, the ant's total displacement is approximately 4.853cm, which is the magnitude of the displacement.