(Solved): questions 5 and 6 4. A relief airplane is delivering a package of food to a group of people stranded ...

4. A relief airplane is delivering a package of food to a group of people stranded on an island that is too small for the plane to land on, and so the only way to deliver the package is by dropping it. The airplane/package flies horizontally with constant speed of \( 411 \mathrm{~km} / \mathrm{hr} \) at an altitude of \( 777 \mathrm{~m} \) (15 pts). (a) Draw a graph of \( v_{x} \), the horizontal velocity, as a function of time. Include units on both axes. (b) Draw a graph of \( v_{y} \), the vertical velocity, as a function of time. Include units on both axes. (c) If the package is to land right on the island, at what horizontal distance from the plane to the island should the package be released? 5. On the Spanish island of La Palma, an impressive new volcano erupted last year that experienced occasional explosive eruptions. During a particular explosive episode, a lava bomb was propelled out of the volcano at \( 88.2 \mathrm{~m} / \mathrm{s} \) at an angle \( 50.0^{\circ} \) to the horizontal ground. Assuming the projectile hits the ground at the same height it started from, how far away from the volcano did it land? (12 pts) 6. During a field goal attempt, a football is kicked such that it leaves the player's foot at \( 22.1 \mathrm{~m} / \mathrm{s} \) at an angle of \( 30.0^{\circ} \) from a location \( 40.0 \) yards from the goalpost. For the field goal to be successful, the football must clear the crosshar, \( 10.0 \mathrm{ft} \) (about \( 3.05 \mathrm{~m} \) ) above the ground. Does the football make it over the crossbar of the goalpost? If so, by how much? If not, by how much does it miss (12 pts)?