document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177283>Question 1177283</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4. An airplane diving at an angle of 40.9º below the horizontal drops a mailbag from an <BR>\n" );
document.write( "altitude of 900 m. The bag strikes the ground 5.00 s after its release. <BR>\n" );
document.write( "a) What is the speed of the plane?<BR>\n" );
document.write( "b) How far does the bag travel horizontally during its fall?<BR>\n" );
document.write( "c) What are the horizontal and vertical components of its velocity just before it <BR>\n" );
document.write( "strikes the ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850484 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's solve this problem step-by-step.\r<BR>\n" );
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document.write( "**Given Information:**\r<BR>\n" );
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document.write( "* Angle (θ): 40.9° below the horizontal<BR>\n" );
document.write( "* Altitude (y): 900 m<BR>\n" );
document.write( "* Time (t): 5.00 s\r<BR>\n" );
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document.write( "**a) What is the speed of the plane?**\r<BR>\n" );
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document.write( "1.  **Vertical Motion:**<BR>\n" );
document.write( "    * We can use the kinematic equation: y = v₀y * t + (1/2) * g * t²<BR>\n" );
document.write( "    * Where:<BR>\n" );
document.write( "        * y = vertical displacement (900 m)<BR>\n" );
document.write( "        * v₀y = initial vertical velocity<BR>\n" );
document.write( "        * g = acceleration due to gravity (9.8 m/s²)<BR>\n" );
document.write( "        * t = time (5.00 s)\r<BR>\n" );
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document.write( "2.  **Calculate Initial Vertical Velocity (v₀y):**<BR>\n" );
document.write( "    * 900 = v₀y * 5 + (1/2) * 9.8 * 5²<BR>\n" );
document.write( "    * 900 = 5v₀y + 4.9 * 25<BR>\n" );
document.write( "    * 900 = 5v₀y + 122.5<BR>\n" );
document.write( "    * 777.5 = 5v₀y<BR>\n" );
document.write( "    * v₀y = 155.5 m/s\r<BR>\n" );
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document.write( "3.  **Calculate Speed of the Plane (v₀):**<BR>\n" );
document.write( "    * v₀y = v₀ * sin(θ)<BR>\n" );
document.write( "    * v₀ = v₀y / sin(θ)<BR>\n" );
document.write( "    * v₀ = 155.5 / sin(40.9°)<BR>\n" );
document.write( "    * v₀ = 155.5 / 0.6549<BR>\n" );
document.write( "    * v₀ ≈ 237.44 m/s\r<BR>\n" );
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document.write( "**b) How far does the bag travel horizontally during its fall?**\r<BR>\n" );
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document.write( "1.  **Calculate Initial Horizontal Velocity (v₀x):**<BR>\n" );
document.write( "    * v₀x = v₀ * cos(θ)<BR>\n" );
document.write( "    * v₀x = 237.44 * cos(40.9°)<BR>\n" );
document.write( "    * v₀x = 237.44 * 0.7558<BR>\n" );
document.write( "    * v₀x ≈ 179.46 m/s\r<BR>\n" );
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document.write( "2.  **Calculate Horizontal Distance (x):**<BR>\n" );
document.write( "    * x = v₀x * t<BR>\n" );
document.write( "    * x = 179.46 * 5.00<BR>\n" );
document.write( "    * x ≈ 897.3 m\r<BR>\n" );
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document.write( "**c) What are the horizontal and vertical components of its velocity just before it strikes the ground?**\r<BR>\n" );
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document.write( "1.  **Horizontal Velocity (vx):**<BR>\n" );
document.write( "    * vx = v₀x (horizontal velocity remains constant)<BR>\n" );
document.write( "    * vx ≈ 179.46 m/s\r<BR>\n" );
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document.write( "2.  **Vertical Velocity (vy):**<BR>\n" );
document.write( "    * vy = v₀y + g * t<BR>\n" );
document.write( "    * vy = 155.5 + 9.8 * 5<BR>\n" );
document.write( "    * vy = 155.5 + 49<BR>\n" );
document.write( "    * vy = 204.5 m/s\r<BR>\n" );
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document.write( "**Answers:**\r<BR>\n" );
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document.write( "* **a) The speed of the plane is approximately 237.44 m/s.**<BR>\n" );
document.write( "* **b) The bag travels approximately 897.3 m horizontally.**<BR>\n" );
document.write( "* **c) The horizontal component of the velocity is approximately 179.46 m/s, and the vertical component is 204.5 m/s.**<BR>\n" );
document.write( " </SPAN>\n" );
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