Question

In an attempt to save the life of a kitten, it is launched out of a window of a burning building at 20 m/s at an angle of 35o to the horizontal. If the window is 25 m above the ground, and there is a firefighter standing 10 m away from the wall of the building, how fast does the firefighter need to run and in what direction—towards or away from the building—in order to catch the kitten just before it strikes the ground?

Answer 1

$$h+v_0\sin{35}t-0.5gt^2=0$$

$$25+20\sin{35}t-0.5(9.8)t^2=0$$

Time of flight:

$$t=3.71\ s$$

The finsl distance of the cat from the wall:

$$s=v_0\cos{35}t=20\cos{35}(3.71)=60.8\ m$$

The firefighter need to run away from the building with speed:

$$u=\frac{s-d}{t}=\frac{60.8-10}{3.71}=13.7\frac{m}{s}$$