47. A baseball is hit so that it travels straight upward after being
struck by the bat. A fan observes that it takes 3.00 s for
the ball to reach its maximum height. Find (a) its initial
velocity and (b) the height it reaches.
\(y_f=h=?\\y_o=0m\\a=-9.8m/s^2\\v_o=?\\v_f=0m/s\\t=3s\)
a) its initial velocity
\(v_f=v_o+at\\0m/s=v_o+(-9.8m/s^2)(3s)\\v_o=\boxed{29.4m/s}\)
\(y_f=h=?\\y_o=0m\\a=-9.8m/s^2\\v_o=?\\v_f=0m/s\\t=3s\)
a) its initial velocity
\(v_f=v_o+at\\0m/s=v_o+(-9.8m/s^2)(3s)\\v_o=\boxed{29.4m/s}\)
(b) the height it reaches.
\(y_f=y_o+v_ot+\frac{at^2}{2}\)
\(h=0m+(29.4m/s)(3s)+\frac{-9.8m/s^2(3s)^2}{2} \\ h=\boxed{44.1m} \)
\(h=0m+(29.4m/s)(3s)+\frac{-9.8m/s^2(3s)^2}{2} \\ h=\boxed{44.1m} \)
