How, if at all, would the equations written in Parts C and E change if the projectile was thrown from the cliff at an angle above the horizontal? Explain your answer.

Answer:

x = v₀ cos θ   t,   y = y₀ + v₀ sin θ t - ½ g t2

Explanation:

This is a projectile launch exercise, in this case we will write the equations for the x and y axes

Let's use trigonometry to find the components of the initial velocity

              sin θ = / v₀

              cos θ = v₀ₓ / v₀

              v_{y} = v_{oy} sin θ

              v₀ₓ = vo cos θ

now let's write the equations of motion

X axis

         x = v₀ₓ t

         x = v₀ cos θ   t

        vₓ = v₀ cos θ

Y axis

        y = y₀ + t - ½ g t2

        y = y₀ + v₀ sin θ t - ½ g t2

        v_{y} = v₀ - g t

       v_{y} = v₀  sin θ - gt

        = v_{oy}^2 sin² θ - 2 g y

As we can see the fundamental change is that between the horizontal launch and the inclined launch, the velocity has components

Final answer:

If a projectile is thrown at an angle above the horizontal, this introduces an additional vertical velocity component. This would affect the equations of Parts C and E by changing the values substituted into them, thereby altering the results for time of flight, highest point, and distance traveled.

Explanation:

If the projectile is thrown from a cliff at an angle above the horizontal, it would introduce a vertical component to the initial velocity in the equations. The equations of motion in Parts C and E would therefore need to incorporate this changed initial velocity.

In the equations, the initial vertical velocity is usually denoted by Vi*sin(θ), where θ is the angle at which the projectile is launched. Similarly, the horizontal velocity is expressed as Vi*cos(θ).

This additional vertical component would affect the time of flight, the height reached by the projectile, and the horizontal distance traveled before it hits the ground. Thus, while the form of the equations might not change, the values substituted into them would.

Learn more about Projectile Motion here:

brainly.com/question/20627626

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