The height of the cliff from the ground is 19.6 meters.
<h3>What is Projectile motion?</h3>
Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration due to gravity.
Given is the initial speed of soccer ball kicked horizontally off a cliff which is 8 m/s. It cover a horizontal distance of 16 m. From this, we can write -
Horizontal initial velocity = u [h] = 8m/s
Horizontal distance covered = S [h] = 16m
For horizontal direction, of motion, we can write -
u [h] = 8m/s
S [h] = 16m
From second equation of motion applied for the horizontal direction -
S[h] = u[h] x t + 1/2 a[h] x t²
Since horizontal acceleration a[h] is zero, we can write -
t = S[h]/u[h]
t = 16/8
t = 2 seconds
Since the ball is kicked horizontally, the initial vertical velocity u[v] will be 0 m/s.
The acceleration in the vertical direction a[v] is directed vertically downwards and is equal to 9.8 m/s².
From second equation of motion applied for the vertical direction -
S[v] = u[v] x t + 1/2 x a[v] t²
S[v] = 1/2 x a[v] t² {u[v] = 0}
S[v] = 1/2 x 9.8 x 4
S(v) = 9.8 x 2
S[v] = 19.6 m
Therefore, the height of the cliff from the ground is 19.6 meters.
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[ The given question is not complete, the complete question is -
A soccer ball is kicked horizontally off a cliff with an initial speed of 8 m/s and lands 16 m from the base of the cliff: What is the time of flight of the soccer ball? What is the height of the cliff? ]
