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

Answer:

B. $100 = 132.12sin2\theta$

Step-by-step explanation:

Given the horizontal distance in meters traveled by a projectile modeled by the function $h = \frac{v_o^{2} }{4.9}sin\theta cos\theta$. 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;

$h = \frac{v_o^{2} }{4.9}sin\theta cos\theta$

from trigonometry identity,

$sin2\theta = 2sin\theta cos\theta\\sin\theta cos \theta = \frac{sin2\theta}{2}$

The equation will become;

$h = \frac{v_o^{2} }{2*4.9}(sin2\theta)$

$h = \frac{v_o^{2} }{2*4.9}sin2\theta$

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

$100 = \frac{36^{2} }{9.8}sin2\theta\\100*9.8 = 1296sin2\theta\\100 = \frac{1296}{9.8} sin2\theta\\100 = 132.12sin2\theta$

Answer 2

Answer:

132.12sin(2theta)=100

Step-by-step explanation: