You would like to shoot an orange out of a tree with your bow and arrow. The ora

Question

You would like to shoot an orange out of a tree with your bow and arrow. The orange is hanging 5.00 m above the ground. On your first try, you fire the arrow at 32.0 m/s at an angle of 30.0 above the horizontal from a height of 1.10 m while standing 42.0 m away. Treating the arrow as a point projectile and neglecting air resistance, what is the height of the arrow once it has travelled the 42.0 m horizontally to the tree? Number If you fire at the same speed and angle on your second try, how far away could you stand such that the arrow will hit the orange? Select all that apply. 7.4 m 47.7 m 83.0 m 13.1 m 77.3 m 5.00 m 30.0 42.0 m 1.10 m

Explanation / Answer

along horizantal

vox = vo*cos30

ax = 0

dixplacement x = 42 m

time taken = x/vox = 42/(32*cos30) = 1.52 s

along vertical

initial velocity = voy = vo*sin30 = 16 m/s

ay = -g = -9.8 m/s^2

from equations of motion

y-yo = voy*t + 0.5*g*t^2

y-yo = 16*1.52 - 0.5*10*1.52^2 = 12.9

y = 12.9+1.1 = 14 m

+++++++

along horizantal

x = vox*t

t = x/vox = x/27.7

for y = 5

y-yo = voy*t + 0.5*g*t^2

3.9 = 16*x/27.7 - 0.5*9.8*(x/27.7)^2

x = 83 m<<<<----answer

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