h=-16t^2+48t describes the rocket's height,h, in feet, from the ground, t seconds after it was launched. A. What is the height of the rocket after 2 seconds. B. After how long will it take the rocket to return to the ground.
simply sub t = 2 into your equation and do the math.
at ground level, h = 0
0 = -16t^2 + 48t
16t^2 - 48t = 0
t^2 - 3t = 0
t(t-3) = 0
t = 0 ---> at the start it is at ground level
or
t = 3
state your conclusion
A. To find the height of the rocket after 2 seconds, we need to substitute t = 2 into the equation h = -16t^2 + 48t.
h = -16(2)^2 + 48(2)
h = -16(4) + 96
h = -64 + 96
h = 32
Therefore, the height of the rocket after 2 seconds is 32 feet.
B. To find when the rocket will return to the ground, we need to determine the value of t when h = 0. This is because when the rocket is on the ground, its height is zero.
0 = -16t^2 + 48t
To solve this equation, we can factor out -16t:
0 = -16t(t - 3)
Setting each factor equal to zero:
-16t = 0 or t - 3 = 0
Solving each equation:
t = 0 or t = 3
Therefore, it will take the rocket 3 seconds to return to the ground.
A. To find the height of the rocket after 2 seconds, we need to substitute t = 2 into the equation h = -16t^2 + 48t:
h = -16(2)^2 + 48(2)
Simplifying this equation, we get:
h = -16 * 4 + 48 * 2
h = -64 + 96
h = 32
Therefore, the height of the rocket after 2 seconds is 32 feet.
B. To find out how long it will take for the rocket to return to the ground, we need to determine when the height (h) becomes zero. This is because when the rocket touches the ground, its height is zero.
Setting h = 0 in the equation -16t^2 + 48t = 0, we have:
-16t^2 + 48t = 0
Next, we can factor out a common term from this equation:
t(-16t + 48) = 0
Since we have a product of two factors equalling zero, we can set each factor equal to zero and solve for t:
t = 0 [one of the possible solutions]
-16t + 48 = 0
-16t = -48
t = (-48)/(-16)
t = 3
Therefore, it will take the rocket 3 seconds to return to the ground.