Spitting cobras can defend themselves by squeezing muscles around their venom glands to squirt venom at an attacker. suppose a spitting cobra rears up to a height of 0.440 m above the ground and launches venom at 3.10 m/s, directed 47.0° above the horizon. neglecting air resistance, find the horizontal distance (in m) traveled by the venom before it hits the ground.

1.289 m

Explanation:

The path the cobra's venom follows since it is spitted until it hits the ground, is described by a parabola. Hence, the equations for parabolic motion (which has two components) can be applied to solve this problem:

x-component:

 (1)

Where:

is the horizontal distance traveled by the venom

is the venom's initial speed

is the angle

is the time since the venom is spitted until it hits the ground

y-component:

  (2)

Where:

 is the initial height of the venom

 is the final height of the venom (when it finally hits the ground)

 is the acceleration due gravity

Let's begin with (2) to find the time it takes the complete path:

  (3)

Rewritting (3):

  (4)

This is a quadratic equation (also called equation of the second degree) of the form , which can be solved with the following formula:

(5)

Where:

Substituting the known values:

(6)

Solving (6) we find the positive result is:

(7)

Substituting (7) in (1):

 (8)

We finally find the horizontal distance traveled by the venom: