15a. A body of mass 15kg is suspended at a point P by two light inextensible strings XP\(^→\) and YP\(^→\). The strings are inclined at 60º and 40º, respectively, to the downward vertical. Find, correct to two decimal places, the tension in the strings (take g = 10m/s\(^2\))

b. The height h metres, of a ball thrown into the air is 2 + 20t + kt\(^2\), after t seconds. If its takes 2 seconds for the ball to reach its height point, Find:

i. the value of k

ii. its highest point from the point of throw.

16a. A ball P moving with velocity 2 u m/s, collides with a similar ball Q, of different mass, which is at rest. After the collision, Q moves with u m/s and P with velocity \(\frac{1}{2}\) u m/s in the opposite direction. Find the ratio of the mass of P and Q.

b. Two forces of magnitude 3N and 7N have a resultant of magnitude 5N. Calculate, correct to one decimal place, the angle between the two forces.

c. AB\(^→\)  \(\left| \begin{array}{cc} -4 \\ 6 \end{array} \right|\) and CB\(^→\)  \(\left| \begin{array}{cc} 2 \\ 3 \end{array} \right|\) are two vectors in the XY plane. If V is the midpoint AB\(^→\). Find CV\(^→\)

17a. A body of mass 5 kg is placed on a smooth plane inclined at an angle of 30º  to the horizontal. Find: the magnitude of the force acting parallel to the plane.

bi. A uniform plank PQ of length 10m and mass m kg rests on two support A and B. Where \PA\ = \BQ\ = 1m. A load of mass 8kg is placed on the plank at point C such that \AC\ = 3.5m, if the reaction at B is 100N. Calculate the value of m

bii. the reaction at A [ take g = 10m/s\(^2\)].