document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203587>Question 1203587</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A projectile is launched from ground level with an initial velocity of v0 feet per second. Neglecting air​ resistance, its height in feet t seconds after launch is given by s=-16t^2+v0t . Find the​ time(s) that the projectile will​ (a) reach a height of 288 ft and​ (b) return to the ground when v0=144 feet per second.<BR>\n" );
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document.write( "(b) The projectile returns to the ground after <BR>\n" );
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document.write( "enter your response here ​second(s). </SPAN>\n" );
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document.write( "Part (a)\r<BR>\n" );
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document.write( "s = -16t^2 + v0*t<BR>\n" );
document.write( "s = -16t^2 + 144t<BR>\n" );
document.write( "288 = -16t^2 + 144t<BR>\n" );
document.write( "0 = -16t^2 + 144t - 288<BR>\n" );
document.write( "-16t^2 + 144t - 288 = 0\r<BR>\n" );
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document.write( "We can then factor<BR>\n" );
document.write( "-16t^2 + 144t - 288 = 0<BR>\n" );
document.write( "-16(t^2 - 9t + 18) = 0<BR>\n" );
document.write( "-16(t - 3)(t - 6) = 0<BR>\n" );
document.write( "t-3 = 0 or t-6 = 0<BR>\n" );
document.write( "t = 3 or t = 6\r<BR>\n" );
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document.write( "Or we can use the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"t+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-144%2B-sqrt%28%28144%29%5E2-4%28-16%29%28-288%29%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-144%2B-sqrt%28%28144%29%5E2-4%28-16%29%28-288%29%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plugged in a = -16, b = 144, c = -288\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-144%2B-sqrt%2820736+-+18432%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-144%2B-sqrt%2820736+-+18432%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-144%2B-sqrt%282304%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-144%2B-sqrt%282304%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-144%2B-++48%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-144%2B-++48%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-144%2B48%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-144%2B48%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-144-48%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-144-48%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-96%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-96%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-192%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-192%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+3 ALIGN=MIDDLE  ALT=\"t+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+6 ALIGN=MIDDLE  ALT=\"t+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Either way, the two answers for part (a) are t = 3 and t = 6\r<BR>\n" );
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document.write( "The projectile reaches 288 ft at t = 3 seconds when going upward. <BR>\n" );
document.write( "Upon its downward trajectory, it gets back to a height 288 ft at t = 6 seconds.\r<BR>\n" );
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document.write( "The projectile is above 288 ft for the interval 3 < t < 6. Otherwise, the projectile is at 288 ft or lower.\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "s = -16t^2 + 144t<BR>\n" );
document.write( "-16t^2 + 144t = s<BR>\n" );
document.write( "-16t^2 + 144t = 0<BR>\n" );
document.write( "-16t(t - 9) = 0<BR>\n" );
document.write( "-16t = 0 or t-9 = 0<BR>\n" );
document.write( "t = 0/(-16) or t = 9<BR>\n" );
document.write( "t = 0 or t = 9\r<BR>\n" );
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document.write( "The projectile starts on the ground, so it makes sense that t = 0 is one solution.\r<BR>\n" );
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document.write( "The other solution is t = 9 which is when the rocket returns to the ground again. <BR>\n" );
document.write( "The flight time is 9 seconds.<BR>\n" );
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