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S7. Rain falls with a velocity of $(2−6k)$ where $$ and $k$ 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 $u$ and notices the rain appearing to fall at a $45_{∘}$ angle into her face. What is the velocity of the cyclist? S8. A ball is fired with angle of projection $30_{∘}$ with respect to the horizontal and an initial speed of $20ms_{−1}$ under the action of gravity. Find its position when it is at its greatest height. S9. A $3kg$ 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 $2ms_{−2}$. What is the new tension in the string? 10. A mass of $6kg$ is projected along a mostly smooth horizontal surface with initial velocity $u$. It passes over a rough section, during which time $24J$ of heat is released due to friction. Its final velocity after emerging from this rough section is $4ms_{−1}$. Find its initial velocity $u$.