A model rocket flies up into the sky. When the rocket reaches a height of 500 feet, it starts to fall back down. The rocket's height above the ground in feet can be modeled by the expression 500−16t2, where t is the time in seconds after the rocket starts to fall back down.What does the quantity 16t2 represent in the expression?Choices:(A)the time in seconds it takes for the rocket to fall t feet(B)the time in seconds it takes for the rocket to reach a height of t feet(C)the height in feet of the rocket above the ground after t seconds(D)the distance in feet the rocket has fallen after t seconds
Q. A model rocket flies up into the sky. When the rocket reaches a height of 500 feet, it starts to fall back down. The rocket's height above the ground in feet can be modeled by the expression 500−16t2, where t is the time in seconds after the rocket starts to fall back down.What does the quantity 16t2 represent in the expression?Choices:(A)the time in seconds it takes for the rocket to fall t feet(B)the time in seconds it takes for the rocket to reach a height of t feet(C)the height in feet of the rocket above the ground after t seconds(D)the distance in feet the rocket has fallen after t seconds
Initial Height Explanation: The expression for the rocket's height is 500−16t2. We know that 500 is the initial height, so 16t2 must be related to the change in height over time.
Height Decrease Over Time: Since the rocket is falling, the height decreases over time. The term −16t2 indicates that the height is being reduced by some factor of time squared.
Acceleration Due to Gravity: The number 16 in the term 16t2 is a constant that relates to the acceleration due to gravity, which is approximately 32 feet per second squared. Since the formula is 500−16t2, it means we're taking half of the acceleration due to gravity, which is typical for free-falling objects in a quadratic equation.
Distance Fallen Representation: Therefore, 16t2 represents the distance in feet that the rocket has fallen after t seconds, because it's the part of the expression that changes with time.
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