A projectile passes through a point 20 m above the point of projection at times t = 1 s and t = 3 s. Neglect air resistance and take g = 10 m/s². Its initial vertical component of velocity is:
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Question

A projectile passes through a point 20 m above the point of projection at times t = 1 s and t = 3 s. Neglect air resistance and take g = 10 m/s². Its initial vertical component of velocity is:

G1 Physics · Accepted Answer

Vertical motion satisfies y = uᵧt - 5t². At y = 20 m, the equation is 5t² - uᵧt + 20 = 0, whose roots are 1 s and 3 s. Sum of roots = uᵧ/5 = 4, hence uᵧ = 20 m/s. Therefore option C is correct.