Find vertical distance of missed shot

[hndalama]

Homework Statement

A hunter is aiming a blowgun directly at a bird on a tree branch 4.0 m above the blowgun and 10 m away. If the speed of the dart is 25.0 m/s and the bird stays in place, by what vertical distance will the dart miss the bird?

Homework Equations

s= ut + 0.5at²

The Attempt at a Solution

the angle(b) of the blowgun is
tanb=4/10 b =21.8

in x direction
u = 25cosb =23.2
a=0
s=10
so t=10/23.2 = 0.43

in y direction
t = 0.43
a=-9.8
u= 25sinb = 9.28

s=ut +0.5at²
s= 3.086

vertical distance of miss = 4 - 3.086 = 0.91

My answer is marked wrong but what is wrong with it?

 

[TomHart]

I couldn't see anything wrong with it unless I made the same mistake you did.

 

[TSny]

Your work looks correct. Was a diagram included with the problem? The phrase "10 m away" could mean that the straight line distance between the hunter and the bird is 10 m.

 

[TomHart]

The phrase "10 m away" could mean that the straight line distance between the hunter and the bird is 10 m.

Good point.

 

[hndalama]

Your work looks correct. Was a diagram included with the problem? The phrase "10 m away" could mean that the straight line distance between the hunter and the bird is 10 m.

ah ..ofcourse. Thank you

 

[hndalama]

actually guys, I tried it again and the answer I'm getting is still marked wrong.

the angle(b) of the blowgun is
sinb=4/10 b =23.58

in x direction
u = 25cosb =22.9
a=0
s=10cosb =9.17
so t=9.17/22.9 = 0.4

in y direction
t = 0.40
a=-9.8
u= 25sinb = 10

s=ut +0.5at^²
s= 3.216

vertical distance of miss = 4 - 3.216 = 0.784

again this is marked wrong but what is wrong with it?

 

[TomHart]

I got 0.785 m. Maybe it needs to be a negative number since it hits below the bird.

 

[hndalama]

it can't be negative, the question is asking for the "distance" which is a scalar quantity. And the question is actually a multiple choice question: The given options are:
a. 0.43 m
b. 0.53 m
c. 0.63 m
d. 0.73 m
e. 1.50 m

I picked 0.73 but that was marked wrong

 

[TomHart]

I don't know. Sometimes the "correct" answer is just incorrect.