Question

Projectile Motion Lab

Explain the nature of the plot: distance traveled vs. horizontal velocity. How would it look like? Why would it be linear? The y-intercept is not equal to zero- What is the meaning of a non-zero intercept?

Answer 1

Consider

Velocity at Time t₀ = V₀

Force acting on projectile = F

Horizontal Velocity (x) = V₀ Cos A + (F Cos A)t; where A is the angle of projectile..........................(A)

Distance Traveled (y) = V₀t + 1/2 (F/m) t²...............................(B)

From (A)

V₀ = (x - (F Cos A)t)/Cos A = x/ Cos A - Ft = k₁x - Ft; where k₁ is a constant

therefore equation becomes

y = (k₁x - Ft)t + k₂Ft²; where k₂ is another constant = 1/2m

y = k₁xt - Ft² + k₂Ft²

So for cases where F = 0

y = k₁xt which is a linear equation

Y-intercept will not be linear if F is not Zero.