A monkey of mass 15 kg climbs a rope having one end fixed to the...

Let $T$ be the tension in the rope, which is equal to the force applied by the monkey.

The equation of motion for the monkey moving upwards with acceleration $a$ is given by

$T - mg = ma$

$T = m(g + a)$

Substituting $m = 15 \text{ kg}$, $g = 10 \text{ m/s}^2$, and $a = 1 \text{ m/s}^2$:

$T = 15(10 + 1) = 165 \text{ N}$

To find the time taken to reach the ceiling, use the kinematic equation:

$s = ut + \dfrac{1}{2}at^2$

Given $s = 5 \text{ m}$, $u = 0$, and $a = 1 \text{ m/s}^2$:

$5 = 0 + \dfrac{1}{2}(1)t^2$

$t^2 = 10$

$t = \sqrt{10} \text{ s}$