Question

The velocity of a projectile at the initial point A is (2i+3j) m/s. Its velocity (in m/s) at point B is

• A. -2i-3j
• B. -2i+3)
• C. 2i-3j
• D. 2i+3j

Answer 1

The Correct Option is C

 To solve the problem of determining the velocity of a projectile at point B, we need to comprehend the properties of projectile motion. In projectile motion, the horizontal component of velocity remains constant as there is no acceleration in the horizontal direction (ignoring air resistance). However, the vertical component of velocity changes due to the acceleration caused by gravity (denoted by \( g \)).

Let's break down the given motion:

1. Initial Velocity: The initial velocity at point A is \( \vec{v}_A = 2\mathbf{i} + 3\mathbf{j} \, \text{m/s} \).
   • The horizontal component is \( v_{Ax} = 2 \, \text{m/s} \).
   • The vertical component is \( v_{Ay} = 3 \, \text{m/s} \).
2. Horizontal Velocity: This remains constant, \( v_{Bx} = v_{Ax} = 2 \, \text{m/s} \).
3. Vertical Velocity at Point B:
   • At the highest point of the projectile's path, the vertical velocity will be zero, and then it reverses direction as the projectile descends.
   • Given that the vertical component of velocity changes linearly with time due to the constant acceleration by gravity, at point B (symmetric point to A vertically), the vertical component of velocity will have the same magnitude but opposite direction to what it was initially.
4. Total Velocity at Point B: Combining these components, the velocity at point B is: \(\vec{v}_B = v_{Bx}\mathbf{i} + v_{By}\mathbf{j} = 2\mathbf{i} - 3\mathbf{j} \, \text{m/s}\)

Therefore, the correct answer is 2i - 3j, which corresponds to the option

2i-3j

.