Consider the crossbow bolt of Example 3, shot straight upward from the ground (y = 0) at time t = 0 with initial velocity v₀ = 49 m/s. Take g = 9.8 m/s² and ρ =  0.0011 in Eq. (12). Then use Eqs. (13) and (14) to show that the bolt reaches its maximum height of about 108.47 m in about 4.61 s.

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ap dt -g-pu² = -8 (1 + 20²). (12)