in a rocket launching, the height h meter, the rocket reaches after t sec for the moment it was launched is given by h=xt-yt
the rocket altitude after 2 sec is 40 metres, and after 3 sec is 45 metres.
a. find x and y
b. altitude rocket after 5 sec
40 = 2 x - 2 y
45 = 3 x - 3 y
120 = 6 x - 6 y
090 = 6 x - 6 y
inconsistent, no solution
To find the values of x and y in the given equation h = xt - yt, we'll use the information provided about the rocket's altitude at 2 and 3 seconds.
a. To find x and y:
Given:
h = xt - yt
Using the information at 2 seconds:
h = 40 meters
t = 2 seconds
Substituting the values into the equation:
40 = 2x - 2y ---(Equation 1)
Using the information at 3 seconds:
h = 45 meters
t = 3 seconds
Substituting the values into the equation:
45 = 3x - 3y ---(Equation 2)
Now, we have a system of equations (Equation 1 and Equation 2) that we can solve to find the values of x and y.
To solve the system of equations, we can use the method of elimination or substitution. Let's use the method of elimination:
Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate y:
120 = 6x - 6y ---(Equation 3)
90 = 6x - 6y ---(Equation 4)
Subtract Equation 4 from Equation 3:
120 - 90 = (6x - 6y) - (6x - 6y)
30 = 0
Since 30 = 0 is not a true statement, it means the system of equations is inconsistent. In other words, there is no unique solution for x and y. This suggests that the given information may have inconsistencies or errors.
b. To find the altitude of the rocket after 5 seconds, we'll use the given equation h = xt - yt.
Let's substitute t = 5 seconds into the equation:
h = x(5) - y(5)
h = 5x - 5y
Since we don't have the values of x and y, we can't determine the exact altitude at 5 seconds without those values.