An archer stands a horizontal distance d= 55 m away from a tree sees an apple hanging from the tree at h= 12 m above the ground. The archer chooses an arrow and prepares to shoot. The arrow is initially 1.5 m above the ground. Just as the archer shoots the arrow with a speed of 80 m/s , the apple breaks off and falls straight down. A person of height 2.0 m is standing directly underneath the apple. The arrow pierced the apple. Ignore air resistance, and use g=9.81 m/s2 for the acceleration of gravity.
What angle did the archer aim the arrow? enter your answer in degrees

Question

An archer stands a horizontal distance d= 55 m away from a tree sees an apple hanging from the tree at h= 12 m above the ground. The archer chooses an arrow and prepares to shoot. The arrow is initially 1.5 m above the ground. Just as the archer shoots the arrow with a speed of 80 m/s , the apple breaks off and falls straight down. A person of height 2.0 m is standing directly underneath the apple. The arrow pierced the apple. Ignore air resistance, and use g=9.81 m/s2 for the acceleration of gravity.
What angle did the archer aim the arrow? enter your answer in degrees

anonymous · Answer

Hey this is from Edx... :P.. plz don't answer this.. you are not supposed to get outside help .. code of conduct dude..

anonymous · Answer

plz i need help

anonymous · Answer

i ll help you.. tell me what part don't u get?!

anonymous · Answer

how to find the angle and at what height should i put ?

anonymous · Answer

i got the distance

anonymous · Answer

u do remember that monkey thing right.. if you aim right at the monkey and while u fire the monkey falls, then it ll hit for sure

so here its given that the arrow hits the apple.. so doesn't it mean, that he aimed right at it?!

anonymous · Answer

yup....so applying rangle formula right? R=

anonymous · Answer

no.. draw it .. u ll get it!

anonymous · Answer

i gt 12 and its wrong

unklerhaukus · Answer

start by drawing it

anonymous · Answer

did that

unklerhaukus · Answer

solve for the time of the apple falling

anonymous · Answer

t=d/v_0cos(thetha)

unklerhaukus · Answer

yeah, you have all those values right?

unklerhaukus · Answer

so get a number for t  and sub it into the arrow equations

anonymous · Answer

i got the arrow pierces apple at a height of 7.97m above persons head

anonymous · Answer

tell me how, if you have got that u can use r=v^2sin2theta/g

anonymous · Answer

Hi super scientist, how did you get the distance I don't want the answer obviously but some guide I am stuck in this one!!

anonymous · Answer

how did u get 7.97 huh?

amistre64 · Answer

my thoughts are:

i would determine an interval of time that it takes the apple to fall from 12m to 2m

the arrow need to cover 55 m at a speed of:  80t cos $\alpha$

amistre64 · Answer

$$0 <=~t~<= \sqrt{\frac{20}{g}}$$

amistre64 · Answer

i determined that by
$$-\frac12gt^2+10=0$$
$$-\frac12gt^2=-10$$
$$gt^2=20$$
$$t^2=\frac{20}{g}$$
$$t=\sqrt{\frac{20}{g}}$$

anonymous · Answer

how did you get a 20 up there

anonymous · Answer

got it

amistre64 · Answer

we can then define a range for the angle knowing the distance and initial velocity of the arrow:$$80t~\cos(\alpha)=55$$
$$\cos(\alpha)=\frac{55}{80t}$$
$$\alpha=\cos^{-1}\left(\frac{55}{80t}\right)$$
t = 0 is out of the question :)  any others we can omit?

amistre64 · Answer

i get a range of angles from 0 to 70 i believe

amistre64 · Answer

lol, i forgot to sqrt my 20/g

amistre64 · Answer

0 to 61

amistre64 · Answer

i would then try to narrow it down by determining how far the arrow would "drop" perse

amistre64 · Answer

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something like this