Answer to Question #172455 in Mechanical Engineering for Diocel Ann Heria

Question

8. A stone has an initial velocity of 200 fps up to

the right at a slope of 4 to 3. The components of

acceleration are constant at a x= -12 fps

and ay= -20 fps. Compute the radius of curvature at the

start and at the top of the path.

Answer 1

V₀ = 200 fps a_x = -12 fps²; a_y = -20 fps²

Since we are given that the acceleration is constant, we can use

v_x = v_0x + a_xt

v_y = v_0y + a_yt 

tan θ = a_y/a_x = -20/(-12) = 5/3

θ = tan^-1(5/3) = 59 degrees

v_0x = v₀*cos θ = 200 fps * cos(59) = 103 fps

v_0y = v₀*sin θ = 200 fps * sin(59) = 171 fps

v_x = 103 - 12t

v_y = 171 - 20t