Question

A man throws a ball vertically upward and it rises through 20 m and returns to his hands. What was the initial velocity (u) of the ball and how much time (T) is remained in the air? (Take $g = 10\, m\, s^{-2}$)

• A. $u = 10\, m\, s^{-1},\, T = 2\, s$
• B. $u = 10\, m\, s^{-1},\, T = 4\, s$
• C. $u = 20\, m\, s^{-1},\, T = 2\, s$
• D. $u = 20\, m\, s^{-1},\, T = 4\, s$

Answer 1

Answer: (D)

Taking vertically upward motion of ball, we have
$\upsilon^{2} = u^{2} + 2gs$
or $0 = u^{2} + 2 \times \left(-10\right)\times 20$ or $u = 20\, m \,s^{-1}$
Taking vertical motion of ball for whole flight,
$S = ut + \frac{1}{2}gt^{2}$
$0 = 20\times t+\frac{1}{2}\times\left(-10\right)\times t^{2}$
$5t^{2} - 20\, t = 0 ⇒ t = 4 \,s.$