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 36.0 m/s at an angle of 30.0° above the horizontal from a height of 1.30 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?

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.

A) 6.8m

B)105m

C)44.6m

D)108m

E)9.4m

Explanation / Answer

here ,

initial speed , u = 36 m/s

angle = 30 degree

let the height is h

h = x * tan(theta) - g*x^2/( 2 * (v * cos(theta))^2) + 1.3

h = 42 * tan(30) - 9.8 * 42^2 /( 2* (36 * cos(30))^2) + 1.3

solving for h

h = 16.65 m

the height of the arrow is 16.65 m

b)

for h = 5 m

h = x * tan(theta) - g*x^2/( 2 * (v * cos(theta))^2) + 1.3

5 = x* tan(30) - 9.8 * x^2 /( 2* (36 * cos(30))^2) + 1.3

solving for x

x = 6.8 m , 107.7 m

the distance from the tree must be 6.8 m , 107.7 m

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