Determine the magnitude of its velocity at s 560 ft Solutio

Determine the magnitude of its velocity at s = 560 ft

Solution

a_t = 0.05 t²

integrating both sides

v = [0.05 / 3] * t³

v = 0.0167 t³

integral ds = integral [0.0167 t³] dt

s = 4.167 * 10^-3 t⁴

550 ft = 4.167 * 10^-3 t⁴

t⁴ = 4.167 * 10^-3 / 550 ft

t = 19.1 s

substitute t in v

v = 0.0167 t³ = 0.0167 * 19.1³= 115 ft/s

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a1 = 115.42 / 240

= 55.5 ft / s²

a_t = 0.05 * 19.1²

= 18.2 ft/s²

a = sqrt [55.51² + 18.2²]

= 58.4 ft/s²