document.write( "Question 193830: Find the height, of a ball, above ground using the following information.
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document.write( "wait 2 seconds, initial velocity is 55 ft/sec, initial height above ground
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document.write( "is 2 ft
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document.write( "Question 1 answers
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document.write( "40 ft
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document.write( "42 ft
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document.write( "46 ft
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document.write( "48 ft \n" );
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Algebra.Com's Answer #145533 by solver91311(24713)![]() ![]() You can put this solution on YOUR website! \r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Technically speaking, you cannot answer this question from the information given. That is because you haven't actually given the initial velocity. Yes, I know that you said the initial velocity is 55 ft/sec, but that is only part of the story. 55 ft/sec is a speed, i.e. a scalar quantity. Velocity is a vector quantity and requires that you specify both the magnitude (speed) and the direction. 55 ft/sec North, 55 ft/sec horizontally, and 55 ft/sec West at a 45 degree angle to the horizontal, are all very different velocities.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Having said all that, I suspect that you really meant that the initial velocity is 55 ft/sec up. So, let's solve the problem using that assumption.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The acceleration due to the force of gravity on an object near the earth's surface is\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Note the minus sign because the accelleration vector is opposite in direction to our velocity vector.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Integrating with respect to time gives the instantaneous velocity at time t:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Where, for this problem, the constant of integration, C, is the initial velocity, and we will call this \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Then integrating the velocity function with respect to time gives the instantaneous height at time t:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Where the constant of integration is the initial height which we will call \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "And substituting the given initial values:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Now the problem is to find \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The only thing left is a little arithmetic.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "John \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " |