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 5.0 m above the ground. You fire the arrow at 32.0 m/s oriented 30.0o above the horizontal from a height of 1.30 m while standing 47.0 m away on your first try. You may neglect air resistance. What is the height of the arrow once it has travelled the 47.0 m horizontally?

I got 14.3 m which is the correct answer, however:

If you fire at the same speed and angle on your second try, how far away can you stand to hit the orange?

hanging 5.0 m above the ground. You fire the arrow at 32.0 m/s oriented 30.0o above the horizontal from a height of 1.30 m while standing 47.0 m away on your first try. You may neglect air resistance. What is the height of the arrow once it has travelled the 47.0 m horizontally? If you fire at the same speed and angle on your second try, how far away can you stand to hit the orange?

Explanation / Answer

Part A)

In the x direction

d = vt

47 = 32(cos 30)t

t = 1.70 sec

In the y

d = vot + .5at^2

d = (32)(sin 30)(1.70) + (.5)(-9.8)(1.70)^2

d = 13.04 m + 1.3 = 14.3 m

Part B)

In the y

3.7 = (32)(sin 30)(t) + (.5)(-9.8)(t^2)

3.7 = 16t - 4.9t^2
In standard form, that is

-4.9t^2 + 16t - 3.7 = 0

Solve in quadratic equation for roots...

The roots are

.25 or 3.01 sec

For distance, we will use the greater time, and then...

d = vt

d = (32)(cos 30)(3.01)

d = 83.5 m

Also, for the lower time you can stand 6.94 m away

In case you need both possible distances, that is 6.94 m and 83.5 m

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