UMUC MATH 140, FALL 2017 QUIZ 4 KOBI SNITZ (1) a short course in Newtonian mechanics: Consider throwing a ball in the air and at an angle with the ground. The velocity v has two components vvert in the vertical direction and vhorz in the horizontal direction. Given that the initial velocity is v0 using some trigonometry the initial vertical velocity is vvert,0 = v0 sin() and the horizontal initial velocity is vhorz,0 = v0 cos(). Due to gravity the vertical velocity is undergoing acceleration so that the vertical velocity at time t is vvert (t) = vvert,0 + gt. 2 The height of the ball is given by h(t) = tvvert,0 + gt2 . What is the maximum height reached by the ball and when does it reach it. Express your answer in terms of , v0 and g. (2) At what time will the ball land back on the ground. That is when will h(t) be zero ? call this time tg and express your answer in terms of , v0 and g. (3) Since there is no horizontal acceleration the horizontal distance traveled by the ball is d(t) = vhorz,0 t how far has the ball traveled horizontally when it lands on the ground. that is at time tg ? express your answer in terms of , v0 and g. (4) The answer you got in question (3) is how far the ball lands when thrown at velocity v0 and angle . Find the angle which causes the ball to land at the largest distance. That is treat your answer to question 3 as a function of and maximize it. (5) on earth the gravitational acceleration g is 10 sm2 how far is it possible to throw a ball if the thrower is able to throw at v0 = 20 m s ? 1