A grandfather clock works by a pendulum system and keeps time because the pendulum has a constant frequency. The grandfather clock in my room has stopped, but I'm too lazy to get out of bed to start the pendulum oscillating again. Hence I throw a sticky piece of gum at the pendulum to get it moving again. My piece of gum has a mass of 10 g, hits the pendulum inelastically with a speed of 10 m/s, and sticks there. Admittedly disgusting. But, more importantly, if the pendulum has a mass of 90 g, how high does the pendulum on my grandfather clock go in meters?

Details and assumptions

• The acceleration due to gravity is $$9.8~m/s^2$$.
• Treat the grandfather clock as a simple pendulum.
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