Two fireworks are set off simultaneously but from different altitudes. The height y in feet of one is
represented by y=-16t^2+120t+10, where t is the time in seconds. The height of the other is represented by y=-16t^2+60t+310. After how many seconds are the fireworks at the same height? ___________ What is
that height? ______________ i really dont get how to do this someone tell me how
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https://www.jiskha.com/questions/1752036/Two-fireworks-are-set-off-simultaneously-but-from-different-altitudes-The-height
To find the time at which the fireworks are at the same height, we need to find the value of t when the two equations are equal. Set the two equations equal to each other:
-16t^2 + 120t + 10 = -16t^2 + 60t + 310
By rearranging the equation, we can simplify it:
-16t^2 + 120t + 10 - (-16t^2 + 60t + 310) = 0
Combine like terms:
-16t^2 + 120t + 10 + 16t^2 - 60t - 310 = 0
Simplify further:
60t - 300 = 0
Now, isolate t by moving the constant term to the other side:
60t = 300
And divide both sides by 60:
t = 300 / 60
Simplifying:
t = 5 seconds
Therefore, the fireworks are at the same height after 5 seconds.
To find the height at that time, substitute this value of t into either of the original equations:
For y = -16t^2 + 120t + 10:
y = -16(5)^2 + 120(5) + 10
Simplifying:
y = -16(25) + 600 + 10
y = -400 + 600 + 10
y = 210 ft
So at 5 seconds, both fireworks will be at a height of 210 feet.