An arrow has an initial launch speed of 38 m/s. If it must strike a target 37 m away at the same elevation, what should be the projection angle?(Hint: sin2θ = 2sinθcosθ)

θ = 14.54°/2 = 7.27°

Therefore, the projection angle θ = 7.27°

Step-by-step explanation:

The range of a projectile can be written as;

R = (v^2 . Sin2θ)/g 1

Where;

R = range = 37m

v = initial speed = 38m/s

θ = projection angle

g = acceleration due to gravity = 9.8m/s^2

Making sin2θ the subject of formula in equation 1

Sin2θ = Rg/v^2

Sin2θ = (37×9.8)/38^2

Sin2θ = 0.2511

2θ = sininverse(0.2511)

2θ = 14.54°

θ = 14.54°/2 = 7.27°

Therefore, the projection angle θ = 7.27°

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional