A scientist invents an antigravity device that shields the region of space above

Question

A scientist invents an antigravity device that shields the region of space above a large metal plate from the earth's gravitational field. Specifically, if the device is turned on at time t=0, the effective magnitude of the gravitational acceleration in the region above the plate decreases exponentially with time according to mag(a)=geqt, where g is the usual gravitational field strength while q is a constant. When enough time has passed that qt becomes large, the effective gravitational field strength above becomes very small compared to original g. Assume q=3, in appropriate SI units.

A) What are the SI units of q?

The scientist keeps a 7 kg bowling ball on a shelf above the plate. The bowling ball becomes loose from the shelf and rolls off and smashes into the plate 1.0 seconds later.

B) If the ball leaves the shelf at essentially vy=0 at time t=0, what is its speed when it smashes into the plate?

C) How high was the shelf holding the ball above the plate?

Explanation / Answer

A) SI unit = t-1

V= Integration( adt)

V= 3.107 m/sec

S= integration(Vdt)

=1.035 meter

I hope this is right.

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