Question

Question 3:Legolas and Gimli are up to their high-jinks on the battle field again. Legolas, having just conquered his first oliphaunt, jumps off its back. He notices an orc lurking a distance 10m below with his bow drawn and aimed right at him. Legolas quickly draws his bow and releases an arrow at the same time as the orc. The arrows collide in mid air and Legolas is able to land safely. We will assume that Legolas is directly above the orc, so that the motion is only vertical. We also assume that the release velocity for orcish bows is 50m/s and the elven bow is twice as good.

a)How long will it take the arrows to collide?Show your work.Hint: When the arrows collide they will be atthe same height.

b)At what height do the arrows collide?Show your work.

Answer 1

we have,

inital distance between Legolas and orc just when the arrows are fired

both Legolas and the orc shoot the arrows at the same time

Let,

the time at which both arrows collide each other

magnitude of vertical displacement of  Leogolas arrow in time   

so we will have,

magnitude of vertical displacement of  orcs arrow in time

we have,

Inital speed of orc's arrow

since, elven arrow is twice as good as orc's arrow, we have,

Inital speed of Legolas'  arrow

acceleration due to gravity directed downward towards ground,

so,

acceleration of the Orc's arrow

(   sign because the arrow shot by orc travels vertical upward in the opposite direction of acceleration due to gravity )

and, acceleration of the Legolas' arrow  

(   sign because the arrow shot by Legolas travels vertical downward in the same direction of acceleration due to gravity )

a )

now for Legolas' arrow the relation between is given by fallowing kinematic relation as,

_____________________________________ relation 1

Similarly,

now for Orc's arrow the relation between is given by fallowing kinematic relation as,

_____________________________________ relation 2

we see that Left hand sides of relations 1 and 2 are same,

so equating right hand sides of relations 1 and 2 we get,

that is time taken for collision of arrows to occure ( expressed in two significant figures )

b )

height above ground the arrows collide magnitude of vertical displacement of  orcs arrow in time

using in   relation 1 we get,

so we get,

height above ground the arrows collide

so,

height above ground the arrows collide ( expressed in two significant figures )