Answer
$(a)\space 5.1\space m$
$(b) \space 1.02\space s$
Work Step by Step
Please see the attached image first.
(a) We know, maximum height occurs at the maximum speed that the package can withstand on the ground.
To find the maximum height of the package, we can apply the equation, $V^{2}=U^{2}+2aS$ to the package as follows.
$\downarrow V^{2}=U^{2}+2aS$
Let's plug known values into this equation.
$(10\space m/s)^{2}= 0^{2}+2\times 9.8\space m/s^{2}\times h$
$100\space m^{2}/s^{2}= 19.6\space m/s^{2}\times h$
$h=\frac{100}{19.6}\space m= 5.1\space m$
To find the maximum height of the package, we can apply the equation, $V=U+at$ to the package as follows.
$\downarrow V=U+at$
Let's plug known values into this equation.
$10\space m/s= 0+ 9.8\space m/s^{2}\times t$
$t= \frac{10}{9.8}\space s= 1.02\space s$
