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A particle is projected vertically upwards with a speed of 40 m/s. At what times...

Further Mathematics
WAEC 2007

A particle is projected vertically upwards with a speed of 40 m/s. At what times will it be 35m above its point of projection? \(\text{Take g} = 10 ms^{-2}\)

  • A. 1 sec and 7 sec
  • B. 1 sec and 8 sec
  • C. 2 sec and 5 sec
  • D. 2 sec and 7 sec
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Correct Answer: Option A
Explanation

\(s = ut + \frac{1}{2}at^{2}\)

\(s = ut - \frac{1}{2}gt^{2}\) (Upward movement against gravity)

\(35 = 40t - \frac{1}{2}10t^{2}\)

\(35 = 40t - 5t^{2}\)

\(5t^{2} - 40t + 35 = 0\)

\(t^{2} - 8t + 7 = 0\)

\((t - 1)(t - 7) = 0 \implies t = \text{1 sec and 7 sec}\)


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