Answer
It takes 21 hours for the ice to melt.
Work Step by Step
We can find the rate of energy absorption of the block of ice;
$\frac{Q}{t} = (1000~W/m^2)\epsilon ~A~cos(\theta)$
$\frac{Q}{t} = (1000~W/m^2)(0.050)(1.0~m^2)~cos(35^{\circ})$
$\frac{Q}{t} = 40.96~W$
We can find the mass of the block of ice;
$m = \rho~V$
$m = (917~kg/m^3)(1.0~m^2)(0.010~m)$
$m = 9.17~kg$
We can find the energy required to melt the ice:
$Q = m~L$
$Q = (9.17~kg)(3.33\times 10^5~J/kg)$
$Q = 3.05\times 10^6~J$
We can find the time it takes to melt the ice:
$t = \frac{Q}{P}$
$t = \frac{3.05\times 10^6~J}{40.96~W}$
$t = 7.45\times 10^4~s$
We can convert this time to units of hours:
$t = (7.45\times 10^4~s)(\frac{1~hr}{3600~s})$
$t = 21~hr$
It takes 21 hours for the ice to melt.
