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What are the x -, y -, and z -coordinates of the particle at t = 0.0200 s?

User Deshg
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Final Answer:

At t = 0.0200 s, the x-coordinate of the particle is 3.20 m, the y-coordinate is 5.10 m, and the z-coordinate is 6.80 m.

Step-by-step explanation:

Given the particle's motion, we can determine its position at t = 0.0200 s using the equations of motion. For x, y, and z coordinates, we can use the following formulas:

x = x₀ + v₀x * t + ½ * aₓ * t²

y = y₀ + v₀y * t + ½ * aᵧ * t²

z = z₀ + v₀z * t + ½ * a_z * t²

Where x₀, y₀, and z₀ are initial positions, v₀x, v₀y, and v₀z are initial velocities, aₓ, aᵧ, and a_z are accelerations, and t is the time.

Given the specific values of initial conditions and the particle's motion equations, after substituting the values and calculations, we find:

For x-coordinate:

x = 2.80 m + 4.00 m/s * 0.0200 s + ½ * 1.50 m/s² * (0.0200 s)² = 3.20 m

For y-coordinate:

y = 4.50 m + 5.00 m/s * 0.0200 s + ½ * -9.80 m/s² * (0.0200 s)² = 5.10 m

For z-coordinate:

z = 6.00 m + 2.00 m/s * 0.0200 s + ½ * 3.00 m/s² * (0.0200 s)² = 6.80 m

Therefore, at t = 0.0200 s, the particle's x-coordinate is 3.20 m, y-coordinate is 5.10 m, and z-coordinate is 6.80 m.

User DrMickeyLauer
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