Answer:
85.14 m
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(y) denotes <em>"in the vertical direction"</em>
(x) denotes <em>"in the horizontal direction"</em>
<u>We are given:</u>
Initial Horizontal velocity of the Ball (u(x)) = 19.8 m/s
Initial height of the ball (s(y)) = 92 m
Initial Vertical velocity of the Ball (u(y)) = 0 m/s
<u>Time taken to reach the ground:</u>
<em>taking downwards direction as positive</em>
Since the horizontal velocity is not opposed by any force, it will be the same until the ball reaches the ground
The vertical velocity will be increasing at a rate of (10 m/s)/s until the ball hits the ground
ay = 10 m/s²
So, while calculating the time. we can just ignore the horizontal velocity
<u>Solving for the time taken:</u>
s(y) = u(y)t + 1/2a(y)t² [second equation of motion]
92 = (0)(t) + 1/2(10)(t)² [replacing the variables]
92 = 5t²
t² = 92/5 [dividing both sides by 5]
t = √18.4 [taking the square root of both sides]
t = 4.3 seconds
So, it took the ball 4.3 seconds to reach the ground
<u>Horizontal Distance travelled by the ball:</u>
We know that the ball will reach the ground in 4.3 seconds
Since the horizontal velocity will not change, the ball will move with a constant velocity of 19.8 m/s in the horizontal direction
<u>Horizontal distance travelled:</u>
s(x) = u(x)t + 1/2a(x)t² [second equation of motion]
s(x) = (19.8)(4.3) + 1/2(0)(t)² [replacing the variables]
s(x) = 85.14 m
Hence, the ball travels 85.14 m horizontally