SOLUTION: If one throws a ball down from a high cliff, the distance it travels can be modeled by the equation: LaTeX: d = -9.8t^2-15t+100 d = − 9.8 t 2 − 15 t + 100 where t is the time

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: If one throws a ball down from a high cliff, the distance it travels can be modeled by the equation: LaTeX: d = -9.8t^2-15t+100 d = − 9.8 t 2 − 15 t + 100 where t is the time      Log On


   

Question 1142926: If one throws a ball down from a high cliff, the distance it travels can be modeled by the equation: LaTeX: d = -9.8t^2-15t+100 d = − 9.8 t 2 − 15 t + 100 where t is the time in seconds and d is the distance in meters.
1. At what time will the ball hit the ground?
2. You will get two answers because this is a quadratic equation. Do both make sense? (Explain in detail Why or Why not).
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+d%28t%29+=+-9.8t%5E2+-+15t+%2B+100+
The ball is thrown downward at +t=0+
+d%280%29+=+-9.8%2A0%5E2+-+15%2A0+%2B+100+
+d%280%29+=+100+ so, the cliff is 100 m high
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What is +t+ when +d%28t%29+=+0+
+-9.8t%5E2+-+15t+%2B+100+=+0+
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+-9.8+
+b+=+-15+
+c+=+100+
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+t+=+%28+15+%2B-+sqrt%28+225+%2B+3920+%29%29%2F%28-19.6%29+
+t+=+%28+15+%2B-+sqrt%28+4145+%29%29%2F%28-19.6%29+
+t+=+%28+15+%2B+64.3817+%29+%2F+%28-19.6+%29+
can't use this result since the answer is negative
++t+=+%28+15+-+64.3817+%29+%2F+%28-19.6+%29+
+t+=+-49.3817+%2F+%28+-19.6+%29+
+t+=+2.5195+ sec
The ball hits the ground in 2.52 sec ( rounded off )
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Note that the problem is not stated correctly.
+d%28t%29+ is not the distance that the ball travels,
but it is the distance above ground from +t+=+0+ sec
to +t+=+2.52+ sec
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Check:
Does +d%28+2.52+%29+=+0+?
+d%28+2.52+%29+=+-9.8%2A2.52%5E2+-+15%2A2.52+%2B+100+
+d%28+2.52+%29+=+-62.234+-+37.8+%2B+100+
+d%28+2.52+%29+=+-100.034+%2B+100+
+d%28+2.52+%29+=+-.034+
The error is due to rounding off
OK