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 0.400 m above the ground and launches venom at 2.80 m/s, directed 39.0° above the horizon. neglecting air resistance, find the horizontal distance (in m) traveled by the venom before it hits the ground.

1.124 m

Explanation:

This situation is a good example of the projectile motion or parabolic motion, and the main equations that will be helpful in this situations are:  

x-component:  

  (1)  

Where:  

is the initial speed  

is the angle at which the venom was shot

is the time since the venom is shot 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

Knowing this, let's begin:

First we have to find from (2):

  (3)

Rearranging (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)

Finally:

  (9)

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