Whole lotta shakin' goin' on. Suppose an earthquake shook a shelf sideways according to x(t) = B sin (ωt) where ω = 2 π f = 2 π/ τ , with f = one cycle per second, and B = 1 meter.
a.) Write symbolic equations for the shelf speed and acceleration versus time.
b.) Estimate the maximum shelf speed and acceleration.
c.) Suppose an object is flung sideways off the shelf at speed vo = 0.1 ω B from height above the floor of h = 2 B. How long, in seconds, does the object take to hit the floor?
d.) What is the horizontal speed of the object just before it hits the floor?
e.) What is the vertical speed of the object just before it hits the floor?
f.) What is the magnitude of the velocity and the direction with respect to the vertical just before the object hits the floor?
g.) What is the distance from the shelf at which the object hits the floor?