A person is standing on a truck is moving with a constant velocity of $15 \mathrm{m} {\mathrm{s}}^{-1}$ on a horizontal road. The man throws a ball in such a way that it returns to his hand after the truck has moved $60 \mathrm{m} \left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$.

A ball is thrown from ground at an angle $\theta$ with horizontal and with an initial speed $u_0$. For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is $V_1$. After hitting the ground, the ball rebounds at the same angle $\mathrm{\theta }$ but with a reduced speed of $\frac{u_0}{\alpha }$. Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is $0.8V_1$, the value of $\mathrm{\alpha }$ is,

A particle has an initial velocity $3\hat{\mathrm{i}}+4\hat{\mathrm{j}}$ and an acceleration of $0.4\hat{\mathrm{i}}+0.3\hat{\mathrm{j}}$. Its speed after $10 \mathrm{s}$ is,