A Stone has an initial velocity of 200 ft per see up to the right at a slope of 4 to 3. The components of acceleration are constant at a_x=-12 ft per second² and a_y=-20 ft per second². Compute the radius of curvature at the start and at the top of the path
V0 = 200 fps ax = -12 fps2; ay = -20 fps2
Since we are given that the acceleration is constant, we can use
vx = v0x + axt
vy = v0y + ayt
tan θ = ay/ax = -20/(-12) = 5/3
θ = tan-1(5/3) = 59 degrees
v0x = v0*cos θ = 200 fps * cos(59) = 103 fps
v0y = v0*sin θ = 200 fps * sin(59) = 171 fps
vx = 103 - 12t
vy = 171 - 20t
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