In the figure,a ball hangs by a very light string.What is the minimum speed of the ball at the bottom of its swing (point B) in order for it to reach point A,which is 1.0 m above the bottom of the swing?

A)2.2 m/s
B)3.1 m/s
C)4.4 m/s
D)4.9 m/s

Question

In the figure,a ball hangs by a very light string.What is the minimum speed of the ball at the bottom of its swing (point B) in order for it to reach point A,which is 1.0 m above the bottom of the swing?

A)2.2 m/s 
B)3.1 m/s 
C)4.4 m/s 
D)4.9 m/s

Quizplus · Accepted Answer

Using conservation of energy:
Potential energy at point B (before release) = mgh
Kinetic energy at point A (at the top of the swing) = 1/2mv^2
Since energy is conserved, we can set them equal:
mgh = 1/2mv^2
Simplifying, we get:
v = sqrt(2gh)
Plugging in the given values, we get:
v = sqrt(2*9.8*1)
v = 4.4 m/s

Therefore, the minimum speed of the ball at the bottom of its swing to reach point A is 4.4 m/s, which is answer choice C.

In the Figure,a Ball Hangs by a Very Light String