A ball of mass 300 g is dropped from a height 10 m above a sandy ground. On reaching the ground, it penetrates through a distance 1.5 m in sand and finally stops. The average resistance offered by the sand to oppose the motion is (acceleration due to gravity $$=10 \mathrm{~ms}^{-2}$$)
A mass of 1 kg falls from a height of 1 m and lands on a massless platform supported by a spring having spring constant $$15 \mathrm{~Nm}^{-1}$$ as shown in the figure. The maximum compression of the spring is (acceleration due to gravity $$=10 \mathrm{~ms}^{-2}$$)
A bead of mass 400 g is moving along a straight line under a force that delivers a constant power 1.2 W to the bead. If the bead is initially at rest, the speed it attains after 6 s in $$\mathrm{ms}^{-1}$$
The range of a projectile is 100 m. Its kinetic energy will be maximum after covering a distance of