Question

Robin Hood in showing off his archery skills to Friar Tuck was firing arrows towards apples in an apple orchard. If the arrows he shot left his bow with a velocity of 100 m/s and at an angle of 30^o above the horizontal.

(a)Determine the velocity of the arrows when they reach the maximum height of their flight path.

(b) If one of the arrows which Robin Hood fired was aimed towards an apple tree which Newton was under (contemplating gravity of course), determine whether or not Newton would get hit if he was located 900 m from Robin Hood when the arrow was fired.

Answer 1

a]

At maximum height vertical component of the velocity is zero and the horizontal component is only there,

V=Magnitude of Initial velocity

V_x=Horizontal Velocity [Remains unchanged because there is no acceleration in the horizontal direction]

x=Angle with horizontal

V_x=Vcosx= 100cos(30)= 86.6 m/s

b]

R=Horizontal range of the projectile

R=V²sin(2x)/g= (100²)sin(60)/9.8= 883.7m

As we can see the range of the projectile is 883.7m, and the Newton is 900m away therefore he will not get hit by the bow .