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 November 4th, 2019, 08:08 PM #1 Senior Member   Joined: Jun 2017 From: Lima, Peru Posts: 188 Thanks: 5 Math Focus: Calculus How can I find the speed of a falling object as seen from a car while in motion? The problem is as follows: A car driving in a city has a constant velocity of $15\hat{i}-15\hat{j}\frac{m}{s}$ with respect to the ground in the highway. However at $t=0\,s$ the driver in the car sees a lady in highest floor of a nearby building dropping a bucket which was at rest. Find the instant (in seconds) from which the driver situated in the car will measure the speed of the bucket to be $-15\,i\frac{m}{s}$. You may consider $\vec{g}=-10\,\hat{j}\frac{m}{s^{2}}$The alternatives given on my book are as follows: $\begin{array}{ll} 1.&0.5\,s\\ 2.&1\,s\\ 3.&1.5\,s\\ 4.&2\,s\\ 5.&2.5\,s\\ \end{array}$ How am I supposed to relate the quantity of the velocity and the instant?. The only equation which I can recall for the position of an object falling is: $y(t)=y_{0}+v_{0y}t-\frac{1}{2}at^2$ But in this case I don't know how tall is the building neither of what else could I do or should I need to find what it is being asked. I suspect that I should sum the vectors for the velocity of the car and that of the bucket falling and from then I could find the time. But I don't know which steps should I take to find such time. Can somebody help me here?.  November 4th, 2019, 08:31 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 3,101 Thanks: 1677 $v_b = -10 t \, \hat{j} \, m/s$ $v_c = (15 \hat{i} - 15 \hat{j}) \, m/s$ $-10t \, \hat{j} - (15 \hat{i} - 15 \hat{j}) = -15\hat{i} \, m/s$ $-15\hat{i} - (10t - 15)\hat{j} = -15\hat{i} \, m/s$ $10t -15 = 0 \implies t = 1.5 \, sec$ Tags car, falling, find, motion, object, speed Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Chemist116 Physics 2 November 4th, 2019 03:16 AM Chemist116 Physics 3 November 1st, 2019 11:44 PM Chemist116 Physics 6 November 1st, 2019 05:14 PM Elize Physics 3 May 16th, 2019 04:46 PM Ahsayuni Calculus 5 February 20th, 2012 06:10 PM

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