PHYSICS 218 Exam 1 FALL, 2009 Do not fill out the information below until instructed to do so! Name:__________________________________ Signature:_______________________________ Student ID:______________________________ E-mail:__________________________________ Section Number: _________________________ • You have the full class period to complete the exam. • Formulae are provided. You may NOT use any other formula sheet. • When calculating numerical values, be sure to keep track of units. • You may use blank pages provided with this packet as scratch paper or come up front to get more. • Be sure to put a box around your final answers and clearly indicate your work to your grader. • All work must be shown to get credit for the answer marked. If the answer marked does not obviously follow from the shown work, even if the answer is correct, you will not get credit for the answer. • Clearly erase any unwanted marks. No credit will be given if we can’t figure out which answer you are choosing, or which answer you want us to consider. • Partial credit can be given only if your work is clearly explained and labeled. Put your initials here after reading the above instructions: ________SCORE Part 1 (20) ___________ Part 2 (20) ___________ Part 3 (20) ___________ Part 4 (15) ___________ Total (75)___________Problem 1 (20 points): Short Questions 1. (2 pts) A toy rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 74 m and acquired a velocity of 30 m/s. The rocket continues to rise in unpowered flight, reaches maximum height, and falls back to the ground. The maximum height reached by the rocket is closest to: A. 120 m B. 114 m C. 108 m D. 132 m E. 126 m 2. (6 pts) The position of an object as a function of time is given by x(t)=at3-bt2+ct-d A. Find the instantaneous velocity as a function of time B. Find the instantaneous acceleration as a function of time C. Find the average acceleration from t=0 to t=T 3. (2 pts) A golf ball is hit so that it leaves the ground at 60 degrees above the horizontal and feels no air resistance as it travels. Which of the following statements about the subsequent motion of this ball while it is in the air are true? (There may be more than one correct choice.) A. Its speed is zero at its highest point. B. Its acceleration is always 9.8 m/s2 downward. C. Its forward acceleration is 9.8 m/s2. D. Its acceleration is zero at its highest point. E. Its velocity is zero at its highest point. 4. (2 pts) The x- and y-coordinates of a particle in motion, as functions of time t, are given by: x(t) = 7t2 - 4t + 6 y(t) = 3t3 - 3t2 - 12t – 6 (all numbers is SI units) The smallest magnitude of the acceleration is closest to: A. 15 m/s2 B. 7 m/s2 C. 18 m/s2 D. 21 m/s2 E. 14 m/s2 Name_________________________ Section Number ___________________________5. (2 pts) Shown here are the velocity and acceleration vectors for an object in several different types of motion. In which case is the object slowing down and turning to the right? A. B. C. D. E. 6. (2 pts) A projectile is fired from the origin (at y = 0 m) as shown in the figure. The initial velocity components are v0x =110 m/s and v0y = 62 m/s. The projectile reaches maximum height at point P, then it falls and strikes the ground at point Q. The x-component of the velocity of the shell at point P is closest to: A. zero B. 28 m/s C. 110 m/s D. 83 m/s E. 55 m/s Name_________________________ Section Number ___________________________7. (2 pts) An object moves in a circle of radius R at constant speed with a period t. If you want to change only the period in order to cut the object's acceleration in half, the new period should be: A. 4t B. t/2 C. t 2 D. t/4 E. t / 2 8. (2 pts) Two particles, A and B, are in uniform circular motion about a common center. The acceleration of particle A is 8.8 times that of particle B. The period of particle B is 2.2 times the period of particle A. The ratio of the radius of the motion of particle A to that of particle B is closest to: A. 19 B. 0.25 C. 16 D. 1.8 E. 4.0 Name_________________________ Section Number ___________________________Problem 2 (20 points) A water hose is used to fill a large cylindrical storage tank of diameter D and height 2D . The hose shoots the water at 45 degrees above the horizontal from the same level as the base of the tank and is a distance 6D away (see figure ). For what range of launch speeds v0 will the water enter the tank? Ignore air resistance, and express your answer in terms of D and g. Name_________________________ Section Number ___________________________Problem 3 (20 points) The engineer of a passenger train traveling at vP sights a freight train whose caboose is distance D ahead on the same track. The freight train is traveling at vF in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant deceleration of a, while the freight train continues with constant speed. For what range of decelerations a will the train collision be avoided? Hint: Take x=0 at the location of the front of the passenger train when the engineer applies the brakes. Ignore numbers in the figure, they are not given! Name_________________________ Section Number ___________________________Name_________________________ Section Number ___________________________Problem 4 (15 points) In an action-adventure film, the hero is supposed to throw a grenade from his car, which is going at velocity vh, to his enemy's car moving with velocity ve. The enemy's car is distance D in front of the hero's car when he lets go of the grenade. You can ignore air resistance, gravitational acceleration is g. A. If the hero throws the grenade so its initial velocity Vgh relative to him is at an angle of 45 degrees above the horizontal, what should the velocity be to have the grenade land into his enemy’s car? The cars are both traveling in the same direction on a level road. B. Find the magnitude of the velocity relative to the earth in terms of Vgh and whatever other givens of this problem you may need to
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