Projectile Motion

Step 1: The general equation of projectile motion is given by: Step 2: Given initial velocity components: Step 3: Using , , and substituting values: Step 4: Therefore, the correct answer is (C).

For projectile motion, the velocity at any point can be broken into two components: horizontal and vertical. The initial velocity is given as at an angle of 45° to the horizontal.
Step 1: Resolve the velocity into horizontal and vertical components.
- The horizontal component of the velocity is: - The vertical component of the velocity is:
Step 2: At the given point, the angle of the velocity vector is 30° to the horizontal. The velocity components at this point are:
- The horizontal velocity remains the same, as horizontal velocity does not change in projectile motion:
- The vertical velocity component is given by: where is the speed at this instant. We will solve for using the equation for vertical velocity in projectile motion. Since vertical velocity changes due to gravity, we can use the fact that the total vertical velocity at this point is given by: At the moment when the angle is 30°, the speed can be determined using the following relation for projectile motion:
Step 3: Simplify: