A hang glider is travelling horizontally at 13 m/s and is located 326 m above the surface of the earth. Suddenly and accidentally a water bottle falls from it. How far will the water bottle travel horizontally?

To find out how far the water bottle will travel horizontally, we need to determine the time it takes for the water bottle to fall from the hang glider. This can be done using the kinematic equation:

š‘‘ = š‘£š‘–š‘›š‘–š‘” + Ā½š‘Žš‘”Ā²

In this equation,
š‘‘ is the vertical distance (326 m),
š‘£š‘– is the initial velocity (0 m/s),
š‘Ž is the acceleration due to gravity (-9.8 m/sĀ²), and
š‘” is the time it takes for the water bottle to fall.

Since the initial velocity of the water bottle is 0 m/s (it starts from rest), we can simplify the equation to:

š‘‘ = Ā½š‘Žš‘”Ā²

Substituting the given values into the equation:

326 m = Ā½(-9.8 m/sĀ²)(š‘”)Ā²

Now, we can solve for time (š‘”):

š‘”Ā² = (326 m) * 2 / (9.8 m/sĀ²)
š‘”Ā² ā‰ˆ 67.35 sĀ²
š‘” ā‰ˆ āˆš67.35 ā‰ˆ 8.21 s

Therefore, it would take approximately 8.21 seconds for the water bottle to fall.

Now, we can find out how far the water bottle will travel horizontally during this time. Since the hang glider is traveling horizontally at a constant speed of 13 m/s, the horizontal distance traveled will be given by the equation:

š‘‘ = š‘£ Ɨ š‘”

Substituting the given values:

š‘‘ = 13 m/s Ɨ 8.21 s
š‘‘ ā‰ˆ 106.73 m

Therefore, the water bottle will travel approximately 106.73 meters horizontally when it falls from the hang glider.

Multiply the time to fall 326 m by the horizontal velocity.