A ball of mass 50
kg and a speed of 5 m/s moves from the position q
= 0^{0} to q
= 30^{0}.
Evaluate the rate at which the ball's speed is decreasing at the
position
q = 30^{0}.

a. 3.95 m/s^{2}
b. 3.35 m/s^{2}
c. 3.60 m/s^{2}
d. 3.00 m/s^{2}

a_{n} = v^{2}/r
= 5^{2}/5
= 5 m/s^{2}
Consider the forces
acting on the ball in the horizontal and vertical directions

T sin q + m a_{n} sin q
= m a_{t} cos q
T cos q
+ m a_{n}
cos q
+ m a_{t}
sin q
= mg

=> 0.5 T + 125 = 43.3 a_{t}
---------- (1)
and 0.866 T + 25 a_{t}
= 490.5 - 216.5 = 274 ---------(2)

Solving
(1) and (2), we have a_{t}
= 3.35 m/s^{2}

The
rate at which the ball's speed is decreasing at
q = 30^{0}
is 3.35 m/s^{2}