Question

Hagar the Horrible is sitting atop the castle wall, holding a large rock. Alphonse the Quick is 25 meters from the wall but moving towards it at 5 meters per second. Assuming that the rock acclerates downwards at 10 meters per second squared, If the wall is 15 meters high, how long after Alphonse starts running towards the wall should Hagar release his rock so that it strikes Alphonse as he arrives? If Hagar throws the rock downwards at 5 meters per second, rather than just dropping it, when should he make his throw?

Answer 1

the time for Hagar to release his rock so that it strikes Alphonse as he arrives is 3.268 s

the time Hagar should throw the rock downward at 5 m/s is 3.6972 s

Explanation:

From the question given; the time taken for Alphonse to reach the castle is :

t = 25m / 5 (m/s)

t = 5 s

Similarly; the time taken by the rock to reach the ground is :

t' =
`(2h)/(g)`

t' =
`(2(15(m)))/(10 m/s^2)`

t' = 1.732 s

Thus; the time for Hagar to release his rock so that it strikes Alphonse as he arrives is
`t_o`:

`t_o = t-t'`

`t_o = (5-1.732)s`

`t_o = 3.268 \ s`

b) We are also being told that the rock is throw downward at 5m/s

i.e u = 5 m/s

Then using the second equation of motion; we have;

`s = ut + (1)/(2)at^2`

`15 = 5t' + (1)/(2)(10)t'^2`

`t' = 1.3028`

`t_o = t-t'`

`t_o = (5-1.3028)s`

`t_o = 3.6972 \ s`

Thus; the time Hagar should throw the rock downward at 5m/s is 3.6972 seconds