Differential Equations Ordinary and Partial Differential Equations Math Forum

 October 22nd, 2009, 06:19 PM #1 Member   Joined: Sep 2009 Posts: 51 Thanks: 0 Differential Equation: Motion Problem A canyon is 1100 meters deep at its deepest point. A rock is dropped from the rim above this point. Write the height of the rock as a function of time t in seconds. (Use -9.8 m/s2 as the acceleration due to gravity.) h(t) = How long will it take the rock to hit the canyon floor? (Give your answer correct to 1 decimal place.) ________s ok so for the first part I got h(t)= -9.8t+1100 do i take the integral of that? or what steps do i take? Thanks October 22nd, 2009, 10:55 PM #2 Senior Member   Joined: Jan 2009 From: Japan Posts: 192 Thanks: 0 Re: Differential Equation: Motion Problem Start with acceleration: a(t) = -9.8 Integrate this to get velocity: v(t) = -9.8t + v0 where v0 is your initial velocity. Here the word "dropped" implies v0 = 0, so v(t) = -9.8t. Integrate this to get position: h(t) = -4.9t^2 + h0 where h0 is your initial height. Here, you are told it is 1100 meters, so h(t) = -4.9t^2 + 1100 To find the time it takes the hit the canyon floor, let h(t) = 0 and find t. October 24th, 2009, 11:38 AM #3 Member   Joined: Sep 2009 Posts: 51 Thanks: 0 Re: Differential Equation: Motion Problem thank you so much for explaining...this really helped Tags differential, equation, motion, problem 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 sivela Differential Equations 1 January 21st, 2011 06:53 PM noul Differential Equations 4 December 19th, 2010 05:34 AM WizKid Differential Equations 4 October 25th, 2010 09:27 PM pippo789 Differential Equations 0 February 21st, 2009 02:32 PM Crumboo Differential Equations 0 November 20th, 2007 04:35 AM

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