45. A ball is thrown vertically upward. It has a speed of 10 m/sec when it has reached one half of its maximum height. How high does the ball rise? Take g = 10 m/s2.

45. A ball is thrown vertically upward. It has a speed of 10 m/sec when it has reached one half of its maximum height. How high does the ball rise? Take g = 10 \(m/s^2\).

(a) 10 m

(b) 5 m

(c) 15 m

(d) 20 m

Answer :  (a) 10 m

\( v^2 = u^2 + 2as \)

\( \text{At maximum height: } v = 0,\ a = -10 \)

\( 0 = u^2 - 2(10)h \)

\( u^2 = 20h \)

\( \text{At } \)\( \frac{h}{2} \)\(:\ v = 10 \)

\( 10^2 = u^2 - 2(10)\)\( \frac{h}{2} \)\( \)

\( 100 = u^2 - 10h \)

\( u^2 = 100 + 10h \)

\( 20h = 100 + 10h \)

\( 10h = 100 \)

\( h = 10 \, \text{m} \)