If the rock is kicked at initial velocity of 12 m/s from a height of 106 m above the ground what horizontal distance does the rock travel before striking the ground?

74 m.

Explanation:

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

Height (h) = 186 m

Initial velocity (u) = 12 m/s

Horizontal distance (d) =?

Next, we shall determine the time taken for the rock to get to the ground. This can be obtained as follow:

Height (h) = 186 m

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

Time (t) =?

H = ½gt²

186 = ½ × 9.8 × t²

186 = 4.9 × t²

Divide both side by 4.9

t² = 186/4.9

Take the square root of both side

t = √(186/4.9)

t = 6.16 s

Thus, the time taken for the rock to get to the ground is 6.16 s

Finally, we shall determine the horizontal distance travelled by the rock as follow:

Initial velocity (u) = 12 m/s

Time (t) = 6.16 s

Horizontal distance (d) =?

Horizontal distance (d) = Initial velocity (u) × Time (t)

d = u × t

d = 12 × 6.16

d = 73.92 ≈ 74 m

Therefore, the horizontal distance travelled by the rock is 74 m

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