The height , h, in feet, of a bottle rocket is modeled by: H = -16t^2 +60t
where t is the time in seconds.
A. Factor the expression.
B. What is the height of the rocket after 2 seconds?
C. What is the height of the rocket after 3.75 seconds? Explain the solution.
A. factor out a 4t
B,C. just plug in the value for t.
C should be easy to explain if you think of what H=0 means.
A. To factor the expression, we can look for common factors of the terms. In this case, the equation is already in factored form.
B. To find the height of the rocket after 2 seconds, substitute t = 2 into the equation:
H = -16(2)^2 + 60(2)
H = -16(4) + 120
H = -64 + 120
H = 56 feet
So, the height of the rocket after 2 seconds is 56 feet.
C. To find the height of the rocket after 3.75 seconds, substitute t = 3.75 into the equation:
H = -16(3.75)^2 + 60(3.75)
H = -16(14.0625) + 225
H = -224.9999 + 225
H ≈ 0.0001 feet
The solution is approximately 0.0001 feet. This means that after 3.75 seconds, the rocket is very close to the ground, almost touching it.
A. To factor the expression, we need to look at the equation: H = -16t^2 + 60t.
First, we can factor out a common factor of -16 from both terms:
H = -16(t^2 - 3.75t).
Next, we can try to factor the quadratic expression inside the parentheses. To do this, we look for two numbers whose product is -3.75 (the coefficient of t) and whose sum is -3.75 (the coefficient of t).
The factors of -3.75 are -3 and 1.25, and their sum is -3.75.
So we can rewrite the expression as:
H = -16(t - 3)(t + 1.25).
Therefore, the factored expression is: H = -16(t - 3)(t + 1.25).
B. To find the height of the rocket after 2 seconds, we substitute t = 2 into the expression:
H = -16(2 - 3)(2 + 1.25)
= -16(-1)(3.25)
= 52 feet.
Therefore, the height of the rocket after 2 seconds is 52 feet.
C. To find the height of the rocket after 3.75 seconds, we substitute t = 3.75 into the expression:
H = -16(3.75 - 3)(3.75 + 1.25)
= -16(0.75)(5)
= -60 feet.
So, according to the given model, the height of the rocket after 3.75 seconds is -60 feet.
However, it's important to note that in reality, a negative height does not make sense in this context, as it implies the rocket is below the ground. So, be cautious when interpreting these values and consider any additional information or constraints that may apply.