Question

A particle located initially at (1.5ˆj+4.0ˆk)m undergoes a displacement of (2.5ˆi+3.2ˆj−1.2ˆk)m. What is the final position of the particle?

a) (4.0, 5.7, 2.8) m
b) (3.5, 7.2, 3.2) m
c) (2.0, 4.8, 1.6) m
d) (1.5, 4.0, 4.0) m

Answer 1

The final position of the particle after the given displacement is (2.5, 4.7, 2.8) m.

Step-by-step explanation:

The student has asked what the final position of a particle is after it undergoes a displacement from its initial position. To find the final position of the particle, we need to add the displacement vector to the initial position vector.

The initial position of the particle is given as (1.5ˆj + 4.0ˆk) m and the displacement is (2.5ˆi + 3.2ˆj - 1.2ˆk) m. Adding the corresponding components, we get:

• Initial x-component is 0i (no i component given), final x-component is 0i + 2.5i = 2.5i m.
• Initial y-component is 1.5j, final y-component is 1.5j + 3.2j = 4.7j m.
• Initial z-component is 4.0k, final z-component is 4.0k - 1.2k = 2.8k m.

Therefore, the final position of the particle is (2.5, 4.7, 2.8) m, which corresponds to one of the options provided in the question.