To find the distance between the two particles after 2 seconds, we can consider their respective velocities and angles of projection. Since the particles are moving at an angle of 60° to each other, we can decompose their velocities into horizontal and vertical components.
Let's denote the first particle as Particle A with an initial velocity of 4 m/s and the second particle as Particle B with an initial velocity of 5 m/s.
Particle A: Horizontal component of velocity (A_x) = 4 m/s * cos(60°) Vertical component of velocity (A_y) = 4 m/s * sin(60°)
Particle B: Horizontal component of velocity (B_x) = 5 m/s * cos(60°) Vertical component of velocity (B_y) = 5 m/s * sin(60°)
Now, let's calculate the horizontal and vertical displacements for each particle after 2 seconds using their respective velocities and the equations of motion:
Particle A: Horizontal displacement (A_dx) = A_x * time = 4 m/s * cos(60°) * 2 s Vertical displacement (A_dy) = A_y * time + (1/2) * g * time^2 = 4 m/s * sin(60°) * 2 s + (1/2) * 9.8 m/s^2 * (2 s)^2
Particle B: Horizontal displacement (B_dx) = B_x * time = 5 m/s * cos(60°) * 2 s Vertical displacement (B_dy) = B_y * time + (1/2) * g * time^2 = 5 m/s * sin(60°) * 2 s + (1/2) * 9.8 m/s^2 * (2 s)^2
To find the distance between the two particles after 2 seconds, we can use the distance formula:
Distance = sqrt((B_dx - A_dx)^2 + (B_dy - A_dy)^2)
Substituting the values and calculating:
Distance = sqrt((5 m/s * cos(60°) * 2 s - 4 m/s * cos(60°) * 2 s)^2 + (5 m/s * sin(60°) * 2 s + (1/2) * 9.8 m/s^2 * (2 s)^2 - 4 m/s * sin(60°) * 2 s)^2)
After evaluating this expression, you can find the distance between the two particles after 2 seconds.