A 50 cm rod rests against a vertical wall with its bottom 30 cm from the wall. The bottom is pulled horizontally away at 4 cm/s. Find the instantaneous downward speed of the top in cm/s (two decimal places).
Let bottom distance be x and top height y. The rigid length gives x²+y²=50². At x=30, y=40 cm. Differentiate: x dx/dt+y dy/dt=0, so dy/dt=−30×4/40=−3 cm/s. The requested magnitude is 3.00.
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