Answer: The second missile will destroy first missile at hieght of 64.76m above the ground at time 19.15475 seconds
Step-by-step explanation:
Step-by-step explanation:
The military is performing missile test,
The one missile is launched from the ground and its path is modeled by the equation as : y= f(x) = [tex]-4(x-10)^2 + 400[/tex]
After 10 seconds, Second heat-seeking missile is launched and its path is modeled by the equation as : y= g(x) = [tex]-2(x-20)^2 + 300[/tex]
After 10 seconds, first missile will be at height of f(10)
f(10) = [tex]-4(10-10)^2 + 400[/tex]
f(10) = [tex]400[/tex]
When both the missile collide each other at same hieght of y
Also. If x is time for f(x) then, time for g(x) will be x-10 such that Second heat-seeking missile is launched after 10 second of first missile is launched
At time of collision, f(x)=g(x-10)
[tex]-4(x-10)^2 + 400 = -2((x-10)-20)^2 + 300[/tex]
[tex]-4(x-10)^2 + 100 = -2(x-30)^2 [/tex]
[tex]2(x-10)^2 - 50 = (x-30)^2 [/tex]
[tex]2[(x)^2-20x+100]- 50 = (x)^2-60x+900 [/tex]
[tex]2(x)^2-40x+200 - 50 = (x)^2-60x+900 [/tex]
[tex]2(x)^2-40x = (x)^2-60x+750 [/tex]
[tex](x)^2=-20x+750 [/tex]
[tex](x)^2+20x-750=0 [/tex]
Roots of x are 19.15475 and -39.1547
Negative time is not possible
Therefore, time at x=19.15475 seconds
And both missiles collide as y=f(19.15475 ) or g(19.15475 -10)
f(x) = [tex]-4(x-10)^2 + 400[/tex]
f(19.15475) = [tex]-4(19.15475-10)^2 + 400[/tex]
f(19.15475) = 64.76m above the ground.
Thus, The second missile will destroy first missile at hieght of 64.76m above the ground at time 19.15475 seconds
