To find the wrecking ball's speed at the lowest point which is suspended from a 5.0 m long cable that makes a 30 degree angle with the vertical. The ball is released and swings down.
To solve this problem, we can use conservation of energy. At the highest point, all of the ball's energy is potential energy (PE=mgh), where m is the mass of the ball, g is the acceleration due to gravity, and h is the height of the ball above its lowest point. At the lowest point, all of the ball's energy is kinetic energy (KE=1/2mv^2), where v is the speed of the ball.
Since energy is conserved, we can set the initial potential energy equal to the final kinetic energy:
mgh = 1/2mv^2
We can cancel out the mass m from both sides, and solve for v:
v = sqrt(2gh)
To find h, we need to use trigonometry to find the height of the lowest point above the ground. The horizontal distance from the point where the ball is released to the point where it reaches its lowest point is given by:
5.0 m * sin(30 degrees) = 2.5 m
The vertical distance from the release point to the lowest point is given by:
5.0 m * cos(30 degrees) = 4.3 m
Therefore, the total height of the lowest point above the ground is:
h = 4.3 m - 0.5 m = 3.8 m
(where we subtract 0.5 m because the ball has a radius of 0.5 m)
Now we can plug in the values for g and h and solve for v:
v = sqrt(2 * 9.81 m/s^2 * 3.8 m) = 3.1 m/s
Therefore, the answer is D) 3.1 m/s.