Answer:
h = 57.6 m
Explanation:
First, we find the linear speed of the ball while in circular motion:
v = rω
where,
v = linear speed of ball = ?
r = radius of circle = length of rope = 1.75 m
ω = angular speed = (3 rev/s)(2π rad/1 rev) = 18.84 rad/s
Therefore,
v = (1.75 m)(18.84 rad/s)
v = 32.98 m/s
Now, we apply the 3rd equation of motion on the ball, when it breaks:
2gh = Vf² - Vi²
where,
g = - 9.8 m/s² (negative sign due to upward motion)
h = height covered = ?
Vf = Final Velocity = 0 m/s (since, the ball finally stops at highest point for a moment)
Vi = Initial Velocity = 32.98 m/s
Therefore,
2(- 9.8 m/s²)h = (0 m/s)² - (32.98 m/s)²
h = ( - 1088.12 m²/s²)/( - 19.6 m/s²)
h = 55.5 m
since, the ball was initially at a height of 2.1 m from ground. So, the total height from ground, will now become:
h = 55.5 m + 2.1 m
<u>h = 57.6 m</u>
