A physics lecturer is demonstrating projectile motion in class. She uses a catapult to fire a ball into the air from a position that is 1 m above the ground. The ball's initial velocity is 9 m/s in a direction that is 40.0 degrees above the horizontal. You may ignore air resistance.

(a) [20 points] The nearest vertical wall in the flight path of the ball is 8 m away in a horizontal direction from the starting position of the ball. Will the ball hit that wall at any point in its flight? (You may assume that the ball does not hit the ceiling.)

(b) [10 points] What should the minimum height of the ceiling be to make sure that the ball does not hit the ceiling? Give your answer to the appropriate number of significant figures.

(b) [2 points] Give an example of a situation in which the average speed of an object is greater in than the magnitude of its average velocity. (c) [15 points] The "2" subway train 30 from Manhattan to Flatbush Avenue is approaching the nal station (Flatbush Avenue) but has stopped on the tracks somewhere outside of Flatbush Avenue. The graph shows the train's velocity as a function of time, from the point just after it begins to move again, up to the point at which it comes to rest at the Flatbush Avenue station. The positive direction of velocity and 0 10 2'0 30 {I'D so 5,, ,0 3'0 9'0 100 displacement is from Manhattan to Timelseconds} Flatbush Avenue along the track. Velocity in miles per hour Give both the magnimde and Sign of each of your numerical answers. (i) What is the train's acceleration from 0 to 10 seconds? And what is its acceleration from 83-89 s? (ii) What is the total displacement of the train from its position at time = zero seconds on the graph? Give your answer in meters, using the conversion 1609 meters = 1 mile. (iii) What is the average velocity (in m/s) of the train over the whole 89-second journey in the graph