SOLUTION: Bob hits a cricket ball into air. The height (in feet) of the ball at time tseconds is given by h(t)=-10.5t^2+66.3t + 6. Find the maximum height the ball reaches and the time in se

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Bob hits a cricket ball into air. The height (in feet) of the ball at time tseconds is given by h(t)=-10.5t^2+66.3t + 6. Find the maximum height the ball reaches and the time in se      Log On


   

Question 962512: Bob hits a cricket ball into air. The height (in feet) of the ball at time tseconds is given by h(t)=-10.5t^2+66.3t + 6. Find the maximum height the ball reaches and the time in seconds when that maximum height occurs
Found 2 solutions by josmiceli, lwsshak3:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h%28t%29+=+-10.5+t%5E2+%2B+66.3t+%2B+6+
The +t+ component of the max height is
found with the formula:
+t%5Bmax%5D+=+-b%2F%282a%29+
where the quadratic has the general form:
+y+=+ax%5E2+%2B+b%2Ax+%2B+c+
You've got +h%28t%29+ instead of +y%28x%29+
+a+=+-10.5+
+b+=+66.3+
+t%5Bmax%5D+=+-66.3%2F%282%2A%28-10.5%29%29+
+t%5Bmax%5D+=+-66.3+%2F+%28+-21+%29+
+t%5Bmax%5D+=+3.16+ sec
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Now find +h%28t%29+=+h%28+3.16+%29+
+h%28t%29+=+-10.5+%2A3.16%5E2+%2B+66.3%2A3.16+%2B+6+
You can finish
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+10%2C+-10%2C+120%2C+-10.5x%5E2+%2B+66.3x+%2B+6+%29+

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Bob hits a cricket ball into air. The height (in feet) of the ball at time tseconds is given by h(t)=-10.5t^2+66.3t + 6. Find the maximum height the ball reaches and the time in seconds when that maximum height occurs
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h(t)=-10.5t^2+66.3t + 6
complete the square:
h(t)=-10.5(t^2-(66.3/10.5)t+(66.3/21)^2)+104.66 + 6
h(t)=-10.5(t-(66.3/21)^2+110.66
The ball reaches the maximum height of 110.7 ft at 3.15 sec