What is the largest possible displacement resulting from two displacements with magnitudes 3 m and 10 m? do you have to use a^2+b^2=c^2
What is the smallest possible resultant?
To find the largest possible displacement resulting from two displacements with magnitudes 3 m and 10 m, you can use the formula of vector addition. The magnitude of the resultant vector can be found using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the two displacements can be thought of as the two sides of a right triangle, and the resultant displacement is the hypotenuse.
So, using the formula a^2 + b^2 = c^2, where a and b are the lengths of the two sides and c is the length of the hypotenuse, we can find the magnitude of the resultant displacement.
For the largest possible displacement, we want to add the magnitudes of the two displacements together. Therefore, the calculation would be:
(3 m)^2 + (10 m)^2 = c^2
9 + 100 = c^2
109 = c^2
Taking the square root of both sides, we find:
c = √109
So, the largest possible displacement resulting from the two displacements with magnitudes 3 m and 10 m is approximately 10.44 m.
Similarly, to find the smallest possible resultant, we would subtract the magnitudes of the two displacements instead of adding them. In this case, the calculation would be:
(10 m)^2 - (3 m)^2 = c^2
100 - 9 = c^2
91 = c^2
Taking the square root of both sides, we find:
c = √91
Therefore, the smallest possible resultant displacement is approximately 9.54 m.