Monday, April 8, 2013

A firecracker tossed into the air at 100 degrees with the horizontal at a speed of a 30 meters per second exploded 15 m away. How long was the...

Well, the first part of the question is easy.  If the firecracker was thrown at a speed of 30 meters per second, then the firecracker exploded at 15 meters, it was in the air for half a second, or .5 seconds.  That can be calculated like this


15 meters   divided by  30 meters/second  =  .5 seconds, or half a second.


The second part of the question is a little harder.  To throw at an angle...

Well, the first part of the question is easy.  If the firecracker was thrown at a speed of 30 meters per second, then the firecracker exploded at 15 meters, it was in the air for half a second, or .5 seconds.  That can be calculated like this


15 meters   divided by  30 meters/second  =  .5 seconds, or half a second.


The second part of the question is a little harder.  To throw at an angle of 100 degrees, that would be a 10 degree angle from the vertical measurement.  If we extend a line straight down from the end of the firecracker's journey, we can do a scale measurement to determine the second line,  which would be the height of the firecracker off the ground.


15 meter hypotenuse,  If we draw it to scale, with 1 centimeter equaling one meter, that would produce a 2.5 meter distance for the base of the triangle, away from the vertical.  Then, using the pythagorean theorem, where c2 = a2 + b2:


225 = 6.25 + b2


225 - 6.25 = 6.25 - 6.25 + b2


218.75 = b2


14.79 meters = b, which would represent the height above the ground the firecracker traveled to before exploding.

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