Section #1: 2D/3D Motion

Question 1

How is the velocity variable V₀x , and V₀y translated in Projectile Motion?

Answer 1

Horizontal: V₀x = V₀cosθ₀
Vertical: V₀y = V₀sinθ₀

Question 2

In Projectile Motion how is change in horizontal and vertical position defined ?

Answer 2

Horizontal:
∆x₀ = (V₀cosθ₀)t

Vertical:
V₀y = (V₀sinθ₀)t - 1/2gt²

Question 3

What is the Equation of the path used when we don’t have a t variable ?

How is it derived?

Answer 3

∆y = tanθ₀x - (gx²)/2V₀cosθ₀²

This equation takes:
∆x₀ = (V₀cosθ₀)t and subs its value of t into ∆y:

t = ∆x₀/V₀cosθ₀ thus:

∆y = ∆x₀(V₀sinθ₀ / V₀cosθ₀) - ½g(∆x₀/sinθ)²

Question 4

What is the equation to Horizontal Range and how is it found ?

Answer 4

R = V₀²sin2θ / g

This equation comes from setting ∆y = 0 and solving for t:

0 = (V₀sinθ)t - ½gt²

½gt² = (V₀sinθ)t → ½gt = (V₀sinθ)

t = 2V₀sinθ / g

This is then subbed into the ∆x equation:

∆x = (V₀cosθ₀)t → 2V₀²cosθ₀sinθ₀ / g

Question 5

Which equation regarding range should be used of t variable is not presented?

Answer 5

R = V₀²sin2θ / g

Question 6

What is the equation of Acceleration in Uniform Circular Motion when Velocity is constant ?

Answer 6

a = V² / r

where r = radius of the circle

Question 7

What is the equation of the Period of Revolution of an object ?

Answer 7

T = 2πr / V

Question 8

What is the equation of Revolutions per Minute ?

Answer 8

rev/min = V / 2πr