A projectile is shot from the ground at an angle of 60 degrees with respect to the horizontal, and it lands on the ground 5 seconds later. Find:

a. the horizontal component of initial velocity
b. the vertical component of initial velocity
c. initial speed

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To find the horizontal and vertical components of the initial velocity, as well as the initial speed, we need to break down the initial velocity into its horizontal and vertical components.

Let's assume that the initial velocity of the projectile is v₀ and that the horizontal component is v₀ₓ and the vertical component is v₀ᵧ.

a. The horizontal component of the initial velocity (v₀ₓ) is given by:
v₀ₓ = v₀ * cos(θ)
where θ is the angle of projection (60 degrees in this case).

b. The vertical component of the initial velocity (v₀ᵧ) can be found using the formula:
v₀ᵧ = v₀ * sin(θ)

c. The initial speed (v₀) can be calculated using the Pythagorean theorem:
v₀ = sqrt(v₀ₓ² + v₀ᵧ²)

Now let's calculate each component.

a. To find the horizontal component of the initial velocity (v₀ₓ), we can use the equation:
v₀ₓ = v₀ * cos(θ)
where v₀ is the initial speed and θ is the angle of projection.

In this case, v₀ₓ = v₀ * cos(60°)

b. To find the vertical component of the initial velocity (v₀ᵧ), we can use the equation:
v₀ᵧ = v₀ * sin(θ)
where v₀ is the initial speed and θ is the angle of projection.

In this case, v₀ᵧ = v₀ * sin(60°)

c. To find the initial speed (v₀), we can use the Pythagorean theorem:
v₀ = sqrt(v₀ₓ² + v₀ᵧ²)

In this case, v₀ = sqrt(v₀ₓ² + v₀ᵧ²)

Now, let's calculate the values.

a. The horizontal component of the initial velocity:
v₀ₓ = v₀ * cos(60°)

b. The vertical component of the initial velocity:
v₀ᵧ = v₀ * sin(60°)

c. The initial speed:
v₀ = sqrt(v₀ₓ² + v₀ᵧ²)

Substitute the given values into the equations and calculate each component.

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