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Answer :
The time taken by the rocket to reach the ground is 8 seconds
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The toy rocket is launched from a platform
The height of the platform = 12 feet
The initial velocity of the rocket = 128 feet / second
Let the height of the launch be = h
Let the time taken by the rocket be = t
The height after the launch after t seconds is given by the equation
h ( t ) = -16t² + 128t + 12
Now , for the rocket to reach the ground , the equation will be
h ( t ) = -16t² + 128t
Since , it is launched from the 12 foot platform , the equation will be
h ( t ) = -16t² + 128t
The height of the rocket on reaching the ground h ( t ) = 0
Substituting the value of h ( t ) in the equation , we get
h ( t ) = -16t² + 128t
0 = -16t² + 128t
16t² - 128t = 0
16t ( t - 8 ) = 0
t - 8 = 0
Adding 8 on both sides , we get
t = 8 seconds
Hence , the time taken by the rocket to reach the ground is 8 seconds
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