hearing rattles from a snake, a boy make two rapid displacements of magnitude 1.8m and 2.4m in sketches show how the two displacements might add up to give magnitude of 4.2m, 3.0m and 0.6m?
1.8+2.4
2.4+2.4-1.8
2.4-1.8
To solve this problem, we can use vector addition. Let's start by visualizing the two consecutive displacements on a sketch. Assume that the first displacement has a magnitude of 1.8m and the second displacement has a magnitude of 2.4m. Refer to the sketch below.
Sketch 1:
```
------------ (1.8m)
|
|
|
------------ (2.4m)
```
Now, we need to add the two displacements together to see if their magnitudes match the given values (4.2m, 3.0m, and 0.6m).
Sketch 2 - Magnitude: 4.2m:
```
------------ (1.8m)
| \
| \
| \
------- ---- (2.4m)
```
In this sketch, we notice that when we add the two displacements together, their resulting magnitude is greater than 4.2m. Therefore, this combination does not match the given magnitude.
Sketch 3 - Magnitude: 3.0m:
```
------------ (1.8m)
|
|
|
----- ------- (2.4m)
```
Here, we see that the sum of the two displacements results in a total magnitude greater than 3.0m. Thus, this combination does not align with the given magnitude.
Sketch 4 - Magnitude: 0.6m:
```
------------ (1.8m)
|
|
|
|
------------ (2.4m)
```
In this sketch, we can observe that the combined magnitude of the two displacements is less than the given value of 0.6m. Therefore, this combination does not satisfy the magnitude requirement.
Hence, based on the sketch analysis, none of the provided combinations of magnitudes (4.2m, 3.0m, and 0.6m) can be achieved by the given displacements of 1.8m and 2.4m.