A juggler throws balls vertically upward with the same speed every 0.5 s. He throws a new ball exactly when the previous ball reaches half of its maximum height while moving upward. Taking g = 10 m s⁻², the launch speed is:
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Question

A juggler throws balls vertically upward with the same speed every 0.5 s. He throws a new ball exactly when the previous ball reaches half of its maximum height while moving upward. Taking g = 10 m s⁻², the launch speed is:

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G1 Physics · Accepted Answer

Maximum height H = u²/(2g). At half height, y = u²/(4g). During ascent: u t − (1/2)gt² = u²/(4g). Put t = 0.5 s and g = 10: 0.5u − 1.25 = u²/40. Multiplying by 40 gives u² − 20u + 50 = 0. Thus u = 10 ± 5√2. The smaller root corresponds to reaching half height after the apex, so the ascending condition requires u = 10 + 5√2 = 5(2 + √2) m s⁻¹.