Question

Define a second angle which will result in the same range for a projectile launched at an angle to the horizontal at 35 degrees?

Answer 1

The range of a projectile is given by the equation
\[R=\frac{ 2v^2\sin(\theta)\cos(\theta) }{ g }\]
So you need to find another angle psi such that\[\sin(\psi)\cos(\psi)=\sin(\theta)\cos(\theta)\]
I think psi and theta are called complementary angles, but i could be wrong

Answer 2

*sigh* i dont know what im doing s: this is my first question like this :/

Answer 3

well you've seen sines and cosines before, right ?

Answer 4

Yes

Answer 5

okay, your condition would be satisfied if sin(psi) = cos(theta) and vice versa

Answer 6

so, what is the sine of zero degrees ?

Answer 7

0?

Answer 8

yes, and what angle has a cosine equal to zero ?

Answer 9

45?

Answer 10

no - do you have a calculator there ?

Answer 11

1 and yes

Answer 12

what do you mean , 1 ?

Answer 13

i put in cos(0)
and i got 1

Answer 14

ah but i don't want the cosine of zero, i want the angle that has its cosine equal to zero

Answer 15

okay, i'll try a slightly different approach

Answer 16

sin of 0 is 0, right ?

Answer 17

Yes

Answer 18

now get cosine 90 off your calculator

Answer 19

-.45

Answer 20

????????????????

Answer 21

D: i put in cos 90 ><

Answer 22

can you just get your calculator to work out the cosine of 90 degrees ?

Answer 23

Hokay.. hopefully its right this time >< is it 0

Answer 24

yes - so sin(0) = cos(90)

Answer 25

now, another pair
work out the sin of 10 degrees for me

Answer 26

would this be a decimal answer

Answer 27

yes

Answer 28

.17

Answer 29

okay , and now work out the cosine of 80 degrees

Answer 30

same thing ?

Answer 31

hmm, interesting

Answer 32

so sin(10) = cos(80)

Answer 33

you seeing the pattern yet ?

Answer 34

Yes aha you go up by 10 degrees for sin you lower 10 for cos

Answer 35

right !
so in general, the two angles add up to 90 degrees

Answer 36

that would be sin 20 cos 70

Answer 37

you got it - so what if one angle was 35 ?

Answer 38

the other would 55

Answer 39

problem solved : )
you should check, work out sin35cos35 and see if it really is the same as sin55cos55

Answer 40

if that's the case, then both angles must have the same range, according to the original formula

Answer 41

Yes this was true

Answer 42

Thank you so much for going through this with me

Answer 43

you're welcome