A toy rocket is launched vertically upward from a 12 foot platform with an
initial velocity of 128 feet per second. Its height h, at time t seconds after
launch is given by the equation h(t) = -16t^2 + 128t +12 . How long will it
take the rocket to reach the ground?

Answers

Answer 1

Answer:

4 mins

Step-by-step explanation:

Answer 2

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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