3. A volcanic eruption occurs from a top of a conical shaped mountain, throwing rocks at various speeds and angles. The slope of the mountain is 15 (or 112 radians) from the horizon, and the mountain stretches over a. large area, so that we may assume it is an innite cone for the purpose of this problem. (a) Assume that a specic rock is being erupted at a speed on and at an angle of a from the horizontal line. Find a parametrization of the trajectory of the rock in terms of time t. Use the y-axis for the vertical line, and the z-axis for the horizontal line, so that the rock's movement is on the zy-plane. (b) Find the time at which the rock lands on the surface of the mountain (as a function of or]. (c) Use your result from (b) to show that the rock will travel a horizontal distance of 21% sin(-1L2 -+- 0:) 003(0) 3: = --. D 9 ~ 006%) where g = 9.8m/s2 is the acceleration due to gravity. (d) Assume that thousands of rocks are being thrown at a speed of 300m/sec, and at angles between 0 10 from the vertical direction (so 80" 90 from the horizontal direction). How far should you stand from the top of the mountain in order to avoid being hit by the rocks? Hint: use the formula: sin(a) cos(b) = :3 (811103 + b) + sin(a - 5)) : in order to maximize 2:0 above, with respect to a