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A cannon is fired from the top of a hill. the height h in feet of the cannonball is defined by the function h(t)=-16t^2+100t+280. Where t represents the time in seconds since the cannonball was fired.

 

Part A. What is the maximum height of the cannonball? Do not enter units for your answer.

Part B. How long before the cannonball strikes the ground? Round to the nearest second.

 Feb 23, 2021
 #1
avatar+34397 
+1

Max height will occur at   t = - b/2a     where    a = -16    b = 100

   use this valueof 't' in the equation to calculate the height max

 

when the cannon ball strikes the ground h = 0

 

0 = - 16t^2 + 100 + 280     Use Quadratic Formula or factoring to find  't'      (throw out negative values of 't')

 Feb 23, 2021
 #2
avatar+964 
0

\(h(t) = -16t^2 + 100t + 280\)

 

Maximum height is at -b/2a = -100/(-32) = 3.125 seconds. Plug that in:

 

\(h(3.125) = \boxed{136.25}\).

 

Part B

 

Use the quadratic formula to find the roots of the quadratic. We get t = -2.0966 or 8.3466. Time can't be negative, so the cannonball is in the air for seconds.

 Feb 23, 2021

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