What is the equation of the line that passes through the point (-1, -7) and has a slope of 2?
1 answer:
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a) 10 sec
b) 256 feet
Step-by-step explanation:
a)
The height of the rocket above the ground at time t is described by the second-order equation
(1)
where:
t is the time, in seconds
h(t) is the height, in feet
represents the initial vertical velocity of the rocket
represents the acceleration due to gravity (downward)
The rocket will return to the ground when the height is zero, so when
Substituting into eq(1) and solving for t, we find:
which has two solutions:
t = 0 (initial instant, so when the rocket starts its motion)
t = 10 s --> this is the time at which the rocket returns to the ground
b)
The height of the rocket is given by
t is the time, in seconds
h(t) is the height, in feet
Here we want to find the height of the rocket after 2 seconds: to do that, we just need to substitute
t = 2 sec
into the equation of the height.
By doing so, we find:
Therefore, the height of the rocket after 2 seconds is 256 feet.