Answer:
2.1 rad/s
Explanation:
Given that,
Mass of a tether ball, m = 0.546 kg
Length of a rope, l = 4.56 m
The maximum tension the rope can withstand before breaking is 11.0 N
We need to find the maximum angular speed of the ball. Let v is the linear velocity. The maximum tension is balanced by the centripetal force acting on it. It can be given by :
Let 
is the angular speed of the ball. The relation between the angular speed and angular velocity is given by :
So, the maximum angular speed of the ball is 2.1 rad/s.
Answer:
4 m/s² down
Explanation:
We'll begin by calculating the net force acting on the object.
The net force acting on the object from the left and right side is zero because the same force is applied on both sides.
Next, we shall determine the net force acting on the object from the up and down side. This can be obtained as follow:
Force up (Fᵤ) = 15 N
Force down (Fₔ) = 25 N
Net force (Fₙ) =?
Fₙ = Fₔ – Fᵤ
Fₙ = 25 – 15
Fₙ = 10 N down
Finally, we shall determine the acceleration of the object. This can be obtained as follow:
Mass (ml= 2.5 Kg
Net force (Fₙ) = 10 N down
Acceleration (a) =?
Fₙ = ma
10 = 2.5 × a
Divide both side by 2.5
a = 10 / 2.5
a = 4 m/s² down
Therefore, the acceleration of the object is 4 m/s² down
Answer:
The rate of change of the shadow length of a person is 2.692 ft/s
Solution:
As per the question:
Height of a person, H = 20 ft
Height of a person, h = 7 ft
Rate = 5 ft/s
Now,
From Fig.1:
b = person's distance from the lamp post
a = shadow length
Also, from the similarity of the triangles, we can write:
Differentiating the above eqn w.r.t t:
Now, we know that:
Rate = 
Thus
