Question

Let h=v0^2/4.9 sin theta cos theta . Model the horizontal distance in meters traveled by a projectile. If the initial velocity is 36 meters/second, which equation would you use to find the angle needed to travel 100 meters? a. 264.49sin(20)=100 b. 132.12sin(20)=100 c. 100sin(20)=100 d. 7.36sin(20)=100

Answer 1

132.12sin(2theta)=100

Explanation:

Answer 2

B.
`100 = 132.12sin2\theta`

Explanation:

Given the horizontal distance in meters traveled by a projectile modeled by the function
`h = (v_o^(2) )/(4.9)sin\theta cos\theta`. If the initial velocity is 36 meters/second, the equation we would you use to find the angle needed to travel 100 meters is shown below;

`h = (v_o^(2) )/(4.9)sin\theta cos\theta`

from trigonometry identity,

`sin2\theta = 2sin\theta cos\theta\\sin\theta cos \theta = (sin2\theta)/(2)`

The equation will become;

`h = (v_o^(2) )/(2*4.9)(sin2\theta)\\`

`h = (v_o^(2) )/(2*4.9)sin2\theta`

Given h = 100 meters and v = 36 m/s

`100 = (36^(2) )/(9.8)sin2\theta\\100*9.8 = 1296sin2\theta\\100 = (1296)/(9.8) sin2\theta\\100 = 132.12sin2\theta`