a projectile is thrown into the air at an angle of 35*..?

Question

and lands on a target that is at the same level the projectile started. It will also land on the target if it is thrown at an angle of:

A.15*
B.25*
C.55*
D.65*

Answer 1

Decompose velocity into vertical and horizontal components
The vertical will give you .5 of time traveled
The horizontal component divided by time will give you range.

Let V be the velocity
Vh=Vcos(35)
Vv=Vsin(35)
Vv=gt
t=Vv/g
range S=Vh (2 t)
Now since we know the range we have to solve for the angle or simply
Let A=35
S=Vh (2 t) = Vh 2 Vv/g or

S= 2 V^2 sin(A) cos(A)

It is true iff sin(A) cos(A)= sin(B) cos(B)

Or B= arcSin(cos(A))= arcCos(sin(A))=
B=arcSin(cos(35))= 55

So it is C

Answer 2

The range of a projectile is given by the equation=u^2sin2a/g
In the above case the range of the projectile is same in both the cases.
The range of the projectile will be the same if they are thrown at angles whose sum is equal to 90.
Therefore in the above case if the projectile is thrown at an angle of 55 then it will hit the target.(90-35=55)

Answer 3

assuming the velocity is the same for both cases.

so lets consider the 35 degree angle first (assuming it's 35 degrees above the horizon)

break it into horizontal and vertical motions.

for horizontal,

d = v (horizontal) x t = v cos (35) x t

for vertical

first note that your throwing the projectile up with a velocity of v x sin (35). it is decelerating due to gravity and has a velocity of 0 at it's max height. then falls to ground again. The time it takes to this = time up + time down and also equals the time it travels horizontally.....

time up...

Vf = Vi + at
0 = v sin(35) + at
t = - v sin (35) / a (where a is negative !)

so the time for horizontal motion = 2 x t = -2 sin (35) / a

that said,,,

d = v cos (35) x (-2) x sin (35) / a

or (a x d / -2) = cos (35) x sin (35)

also note that cos (35) = sin (90-35) = sin (55)
and sin (35) = cos (90-35) = cos (55)

substituting, sin (55) and cos (55) for cos (35) and sin(35) gives....

(a x d / -2) = cos (35) x sin (35) = cos (55) x sin (55)

So the answer is C