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=-16t2+60x+310. After how many seconds are the fireworks at the same height? ___________ What is
that height? ______________
well, just set them equal to each other, so
-16t^2+120t+10 = -16t2+60x+310
immediately the -16t^2 drops out, so you left with
120t+10 = 60x+310
can't get any easier than that
To find the time when the fireworks are at the same height, we need to set the two expressions for height equal to each other and solve for t.
Given:
y = -16t^2 + 120t + 10 (equation 1)
y = -16t^2 + 60t + 310 (equation 2)
Setting equation 1 equal to equation 2:
-16t^2 + 120t + 10 = -16t^2 + 60t + 310
Now, we can simplify the equation by canceling out the -16t^2 terms on both sides:
120t + 10 = 60t + 310
Next, we can collect the t terms on one side and the constant terms on the other side:
120t - 60t = 310 - 10
Simplifying further:
60t = 300
Now, we can divide both sides of the equation by 60 to solve for t:
t = 300 / 60
t = 5
Therefore, the fireworks are at the same height after 5 seconds.
To find the height at that time, we can substitute t = 5 into either equation 1 or equation 2. Let's use equation 1 for example:
y = -16(5)^2 + 120(5) + 10
y = -400 + 600 + 10
y = 210
Therefore, the height of the fireworks when they are at the same height is 210 feet.