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. You fire the arrow at 33.0 m/s oriented 30.0 ° above the horizontal from a height of 1.30 m while standing 54.0 m away on your first try. You may neglect air resistance.

What is the height of the arrow once it has travelled the 54.0 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? Options for this answer are: 13.5m, 6.9m, 89.2m, 60.6m, or 82.6m

Explanation / Answer

time for horizontal displacement= 54m

t * 33* cos30 = 54

t = 1.889 sec

height = 1.3 + 33*sin30 * 1.889 - 4.9*1.889*1.889 = 13.68 1.3 = 14.98 m when it travels 54m horizontal

now calculate time for height = 5-1.3 = 3.7

3.7 = 33*sin30 *t - 4.9 * t^2

t = 0.24 sec , 3.125 sec

it can stand away (0.24 * 33*cos30 = 6.858 m ,,, 3.125*33*cos30 = 89.308 m )

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