(Solved): Step by step please S7. Rain falls with a velocity of (26k) where and k are unit vect ...

Step by step please

S7. Rain falls with a velocity of $(2\hat{\mathbf{ı}}-6\hat{\mathbf{k}})$ where $\hat{\mathbf{ı}}$ and $\hat{\mathbf{k}}$ are unit vectors in the horizontal and vertical directions, respectively. At what angle does the rain hit the ground? A cyclist travels through the rain at $u\hat{\mathbf{ı}}$ and notices the rain appearing to fall at a $45^{\circ }$ angle into her face. What is the velocity of the cyclist? S8. A ball is fired with angle of projection $30^{\circ }$ with respect to the horizontal and an initial speed of $20{\mathrm{ms}}^{-1}$ under the action of gravity. Find its position when it is at its greatest height. S9. A $3\mathrm{kg}$ mass is suspended from a string under gravity. What is the tension in the string? The string is then pulled upwards and the mass accelerates upwards with an acceleration of $2{\mathrm{ms}}^{-2}$. What is the new tension in the string? 10. A mass of $6\mathrm{kg}$ is projected along a mostly smooth horizontal surface with initial velocity $u$. It passes over a rough section, during which time $24\mathrm{J}$ of heat is released due to friction. Its final velocity after emerging from this rough section is $4\mathrm{m}{\mathrm{s}}^{-1}$. Find its initial velocity $u$.