In the figure,point P is at rest when it is on the x-axis.The linear speed of point P when it reaches the y-axis is closest to
A) 0.18 m/s.
B) 0.24 m/s.
C) 0.35 m/s.
D) 0.49 m/s.
E) 0.71 m/s.

Question

In the figure,point P is at rest when it is on the x-axis.The linear speed of point P when it reaches the y-axis is closest to 
A) 0.18 m/s. 
B) 0.24 m/s. 
C) 0.35 m/s. 
D) 0.49 m/s. 
E) 0.71 m/s.

Quizplus · Accepted Answer

Since point P is at rest on the x-axis, its initial velocity is zero. We can use conservation of energy to determine the final velocity of point P when it reaches the y-axis. At any point along the trajectory of point P, we have

$\frac{1}{2}mv^2=mgh$

where m is the mass of the object, v is its velocity, h is its height above the x-axis, and g is the acceleration due to gravity.

When point P reaches the y-axis, its height is h=2a, where a is the length of the sides of the square. Therefore, we have

$\frac{1}{2}mv_y^2 = mg(2a)$

where $v_y$ is the velocity of point P when it reaches the y-axis. Note that we can ignore the gravitational potential energy when point P is on the x-axis since its height is zero.

Solving for $v_y$, we get:

$v_y = \sqrt{4ga}$

Substituting in the given numerical values, we find:

$v_y \approx 0.35 $m/s

Therefore, the closest choice to the linear velocity of point P when it reaches the y-axis is C (0.35 m/s).

In the Figure,point P Is at Rest When It Is