Atetherball is tied to the end of a string of negligible mass. the ball is struck so that it moves in uniform circular motion in a horizontal plane, and the string makes an angle of 26° with the vertical pole. the mass of the ball is 1.3 kg. what is the ball's speed

The centripetal force is directed parallel to the string and the weight of the ball is always directed downwards. Making a force balance along the direction of vertical axis:
Fc cos 26 = W
where Fc is the centripetal force which is equal to mv2/r
W is the weight which is equal to mg

m v2 /r cos 26= mg
v2 /r cos 26 = g
v2 = rg cos 26
v2 = 2.1(9.81) cos 26
v = 4.30 m/s

The ball's speed is 4.30 m/s.

Kinetic energy = 1/2mv^2. since the mass is constant we can form a ratio of it's kinetic energy at 60 divided by that at 30 to see ke(60)/ke(30) = +(60^2)/30^2). this may be said to 300% increase.