CT2-9Part A: A ball is fired from a canon straight upward with an initial velocity vo. Assume no air resistance. If the initial velocity vo is doubled, the time to reach the apex of the trajectory..A: doubles. B: increases by a factor of 4. C: Neither of these.D: Impossible to tell from the information given.Answer: In lecture, we derived the formula for the time to reach the max height: t = vo/g. If vo doubles, then t doubles.Part B: If the initial velocity vo is doubled, the maximum height of the ball..A: doubles. B: increases by a factor of 4. C: Neither of these.D: Impossible to tell from the information given.Answer: In lecture, we derived the formula for max height of the ball: y = vo2 /(2g). If vo doubles, then vo2 increases by a factor of 4. So the max height increases by 4.CT2-11. On planet X, a cannon ball is fired straight upward. The position and velocity ofthe ball at many times are listed below. Note that we have chosen up as the positive direction.Time(s) Height(m) Velocity(m/s)0 0 201 17.5 152 30 103 37.5 54 40 05 37.5 -56 30 -107 17.5 -158 0 -20What is the acceleration due to gravity on Planet X?A: -5m/s2B: -10m/s2C: -15m/s2D: -20m/s2E: None of these.yAnswer: The acceleration is -5 m/s2. (the minus sign is because we chose up as the positive direction). Acceleration a = v/t = (v2 – v1 )/( t2 – t1). Take any pair of points from the table… say the first two points: v1 = 20 m/s, t1 = 0 s and v2 = 15 m/s, t2 = 1s. Then a = (v2 – v1 )/( t2 – t1) = (15 – 20)/(1 – 0) = - 5 m/s2.CT2-13A truck traveling at 20 km/hr approaches a car stopped at a red light. When the truck is 100m from the back of the car, the light turns green and the car immediately begins to accelerate at 2.00m/s2. Which graph below represents this situation?Answer: Graph B. txtxtxA BCD: None of thesecarcarcartrucktruck truckIf the car starts at x = 0 at time t = 0, then the position of the car, as a function of time isxc = (1/2) ac t2 , where ac = acceleration of car. This is the graph of a parabola.The truck has constant velocity vt = constant , zero acceleration (at = 0) , so its position vs. time is xt = xto + vt t . This is the graph of a straight line. At t = 0, the truck is at position xto = -100 m ( negative because it is behind the car).CT2-14A ball is fired from a canon straight upward with an initial velocity vo. Assume no air resistance. If the initial velocity vo is doubled, the time to reach the apex of the trajectory..A: doubles. B: increases by a factor of 4. C: Neither of these.D: Impossible to tell from the information given.If the initial velocity vo is doubled, the maximum height of the ball..A: doubles. B: increases by a factor of 4. C: Neither of these.D: Impossible to tell from the information
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