Answer:
Height of cliff = S = 20 m (Approx)
Explanation:
Given:
Initial velocity = 8 m/s
Distance s = 16 m
Starting acceleration (a) = 0
Computation:
s = ut + 1/2a(t)²
16 = 8t
t = 2 sec
Height of cliff = S
Gravitational acceleration = 10 m/s
S = 1/2a(t)²
S = 1/2(10)(2)²
Height of cliff = S = 20 m (Approx)
Average speed = (total distance covered) / (time to cover the distance)
total distance covered = (4km + 2km + 1km) = 7 km
time to cover the distance = (32min + 22min + 16min) = 70 min
Average speed = (7 km) / (70 min)
Average speed = 0.1 km/minute
The object takes 0.5 seconds to complete one rotation, so its rotational speed is 1/0.5 rot/s = 2 rot/s.
Convert this to linear speed; for each rotation, the object travels a distance equal to the circumference of its path, or 2<em>π</em> (1.2 m) = 2.4<em>π</em> m ≈ 7.5 m, so that
2 rot/s = (2 rot/s) • (2.4<em>π</em> m/rot) = 4.8<em>π</em> m/s ≈ 15 m/s
thus giving it a centripetal acceleration of
<em>a</em> = (4.8<em>π</em> m/s)² / (1.2 m) ≈ 190 m/s².
Then the tension in the rope is
<em>T</em> = (50 kg) <em>a</em> ≈ 9500 N.
