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Learn about the math and science behind what students are into, from art to fashion and more. We are here to help with distance learning resources for schools and districts.
See our latest posts. During the Activity Discuss the materials from the Student Page with your class. After the Activity Encourage students to explore web sites and questions from the Extensions page. Usually credit cards compound monthly, so there are 12 compounding periods per year. After the second month, you'll owe Technically, the term velocity means the vector pointing in the direction of motion with magnitude equal to the speed of the object. However, in everyday usage and even in many physics textbooks the term velocity is used to denote both the vector and its magnitude, the speed.
It is usually easy to figure out which is being meant from the context: just ask yourself, is the sentence talking about a vector or a scalar?
Activity 1: Let us first consider only the vertical direction of motion. For the sake of brevity, I'll just write v t below instead of v vertical t. Recall that the acceleration of an object is equal to the instantaneous change in velocity, i. Apply the fundamental theorem of calculus to this equality to deduce that , where g is the acceleration due to gravity. We can do even better by applying the same trick to velocity. Apply the fundamental theorem of calculus again to show that Now write down an equation for the horizontal position x t of the bullet in terms of the initial horizontal velocity v horizontal 0.
Hint: remember, we disregard drag and wind so the only acting force is gravity. Use the equations from activity 1 to answer the following questions. What is the maximum height achieved by the bullet? At what time is this height achieved? Hint: what is the vertical velocity of the bullet when it's at a peak height? What is the horizontal distance of the bullet from the origin at the time of peak height?
Show that the trajectory of the bullet is a parabola. Megan talks to the widow from the most recent robbery. She points to a lamp that was stolen as the most valuable thing to them. At CalSci Charlie is ranting about Penfield. Megan and David follow up about the lamp with an auctioneer. He got it from a man named Roley. Charlie is caught up in his work. The core team check in on him.
He has the dates of the robberies marked out on maps. He urges them to look at more than just home robberies that fit in the general MO on the other days that he has singled out.
He gives his best guest on when the next home robbery will happen. Three car jackings happened on the other days Charlie marked. Colby is skeptical because they are high end robbers, but Megan lists the cars stolen as high end vehicles: a Mercedes, a Range Rover, and a Porsche. None have been found and they assume that the cars are long gone. A gun was shot during the Porsche jacking. David and Colby are sent to track down the bullet and Megan is sent to track down the fence, Roley. Charlie waits for more data when David and Colby and come and ask him for help finding the bullet.
Penfield shows up and puts his two cents in. Megan finds out that the robbers stole other items during the jackings. Megan finds Roley and they are setting up a sting.
Charlie comes home and finds Alan getting all of his city planning notes out from storage. Charlie is still upset from his earlier dealings with Penfield. Megan is waiting for Roley. They bring down Roley and his muscle. In the storage locker Megan finds the lamp.
She interrogates him at the FBI. He admits to getting the items from the robberies from two guys, but had no part in the murders. They found him in a bar based on his reputation. They now believe this to be a five-man crew - two to case, three to rob.
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