document.write( "Question 481435: a ball in thrown vertically up with a velocity of 10m/s.
\n" ); document.write( "A.determine the time it takes for the ball to reach the maximum height.
\n" ); document.write( "B. the speed by which the ball will fall back to the point from where it was thrown. \n" ); document.write( "

Algebra.Com's Answer #329677 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
The height of an object propelled upwards with an initial velocity $\"v%5B0%5D\"$ from a height $\"h%5B0%5D\"$ is given by the function:
\n" ); document.write( " $\"h%28t%29+=+-4.9t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"$ where: $\"h\"$ is the height (in meters) at time (seconds) $\"t\"$ , $\"v%5B0%5D\"$ is the initial upward velocity (meters per second), and $\"h%5B0%5D\"$ is the initial height (meters) from which the object is thrown.
\n" ); document.write( "A. The graph of this function is a parabola which opens downward and the vertex of the parabola represents the maximum height of the object at time t seconds. So starting with the function:
\n" ); document.write( " $\"h%28t%29+=+-4.9t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"$ Substitute $\"v%5B0%5D+=+10\"$ m/s and $\"h%5B0%5D+=+0\"$ since no initial height was given, we'll assume the ball is thrown from ground-level.
\n" ); document.write( " $\"h%28t%29+=+-4.9t%5E2%2B10t\"$
\n" ); document.write( "The vertex is found by:
\n" ); document.write( " $\"t+=+-b%2F2a\"$ (from $\"at%5E2%2Bbt%2Bc+=+0\"$ )where a = -4.9 and b = 10
\n" ); document.write( " $\"t+=+-%2810%29%2F%282%28-4.9%29%29\"$
\n" ); document.write( " $\"t+=+1.02\"$ seconds. This is the time taken for the ball to reach maximum height.
\n" ); document.write( "B. This part of question does not make sense because while the ball is falling, it is accelerating i.e. the speed is not constant!
\n" ); document.write( "The question would have to state the time (t) at which the speed of the falling object is required. \n" ); document.write( "

\n" );