Homework Hints Chapter 01-03.pdf

30. a) Use trigonometry to find the vertical component of the speed of the projectile. Usewith the vertical deceleration caused by gravity. List our variables and choose fromVAT, VAX, VATX or the Range equation to solve for Δy.b) Now you know v oy , v y , acceleration and height. List your variables and choose fromVAT, VAX, VATX or the Range equation to solve for t. Remember that the total timein the air will be twice the time to go up or come down.c) List your variables and choose from VAT, VAX, VATX or the Range equation tosolve for Δxd) The horizontal velocity is constant and can be found using trigonometry to find thehorizontal component of the speed of the projectile. Use VAT with the verticalcomponent of the velocity as v oy , to find the vertical velocity after 1.5 seconds.31. a) You are given an initial height (Δy). Use the angle and initial velocity to find theinitial vertical velocity. Now you have distance, acceleration (gravity) and initialvelocity. Use VAT, VAX or VATX and solve for time. You can do this in threesteps as in problem #39 of chapter 2, or one, using the quadratic equation.b) Use the angle and initial velocity to find the initial horizontal velocity. The projectiledoes not accelerate horizontally, so use the distance equation and the time frompart a) to find the horizontal distance traveled.c) You now have initial horizontal and vertical velocities, horizontal and verticalacceleration and distances. Choose from VAT, VAX, VATX and the distanceequation to solve for the final velocity of each.d) Use the Pythagorean theorem and the answers from part c.e) Use the tangent function and the horizontal and vertical velocities to find the angle.32. Since the ball does not take off and land at the same level, you can’t use the RangeEquation. Using v o and Θ, find v x and v y . Using v y , g and Δy, use VATX and solve forthe time the ball is in the air. Then use v x , the time and the distance equation to calculatethe horizontal distance traveled.35. a) Find the time it will take the package to fall the vertical distance, and then use thedistance equation and the horizontal velocity to find how far the package will travel inthe time it takes to fall that far.b) From part a), you find that the package will travel farther than 425 meters in the timeit takes to fall, so it needs a push to get to the drop site in time. Use the horizontaldistance (425 meters) given, the horizontal velocity and the distance equation to findthe time the package has to fall. Now you have time, vertical distance, andacceleration. Choose from VAT, VAX or VATX and solve for initial verticalvelocity.c) Use the initial velocity found in part b), vertical acceleration and vertical distance andchoose from VAT, VAX or VATX to find the final velocity.For 36 and 37, the two velocities form the legs of a right triangle. Each problem isasking for the hypotenuse of the triangle.11