The bottle slides down the hill and is moving at a velocity of 14 meters/second the instant it hits the ground. The vertical height from where Jeff dropped the bottle is meters. Ignore friction, and use , PE = m × g × h, and g = 9.8 m/s2.

10 m

Explanation:

From the question given above, the following data were obtained:

Velocity (v) = 14 m/s

Acceleration due to gravity (g) = 9.8 m/s²

Height (h) =?

Next, we shall determine the energy. This can be obtained as follow:

Velocity (v) = 14 m/s

Kinetic Energy (KE) =?

KE = ½mv²

KE = ½ × m × 14²

KE = ½ × m × 196

KE = m × 98

Finally, we shall determine the height. This can be obtained as follow:

Kinetic energy (KE) = m × 98

Acceleration due to gravity (g) = 9.8 m/s²

Height (h) =?

Since the object is falling from a particular height,

Potential energy (PE) = kinetic energy (KE)

PE = mgh

KE = m × 98

m × 9.8 × h = m × 98

Divide both side by m × 9.8

h = m × 98 / m × 9.8

h = 10 m

Thus, the bottle was dropped from a height of 10 m