Jaylen launches his new high-powered model rocket upward during the Rocket Week demonstration. The rocket flies far up into the sky before falling back down to the ground. The rocket has an initial velocity of 147 meters per second. Therefore , the rocket's height above the ground in meters, t seconds after being launched, can be modeled by the expression -4.9t^2+147t This expression can be written in factored form as -4.9t(t-30) What does the number 30 represent in the expression? the time in seconds from when the rocket is launched until it reaches the top of its flight the height in meters of the rocket when it reaches the top of its flight the time in seconds from when the rocket is launched until it hits the ground the height in meters of the rocket when it is launched

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Jaylen launches his new high-powered model rocket upward during the Rocket Week demonstration. The rocket flies far up into the sky before falling back down to the ground. The rocket has an initial velocity of 147 meters per second. Therefore , the rocket's height above the ground in meters, t seconds after being launched, can be modeled by the expression -4.9t^2+147t This expression can be written in factored form as -4.9t(t-30) What does the number 30 represent in the expression? the time in seconds from when the rocket is launched until it reaches the top of its flight the height in meters of the rocket when it reaches the top of its flight the time in seconds from when the rocket is launched until it hits the ground the height in meters of the rocket when it is launched

Answer 1

the time in seconds from when the rocket is launched until it hits the ground

Answer 2

The given expression for the height of the rocket over time is \( -4.9 t^{2} + 147 t \). In its factored form \( -4.9 t(t-30) \), the term \( t-30 \) implies that \( t = 30 \) is a root of the quadratic equation \( -4.9 t^{2} + 147 t = 0 \). <br /><br />This means that when \( t = 30 \), the height of the rocket is zero, indicating the point in time when the rocket returns to the ground after its flight. In other words, it represents the total time from the launch until the rocket hits the ground.

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