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Answer :
We know that v0 is 176 ft/s and h0 is 0 because the rocket is at ground level before launch.
h(t) will also equal 0 when the ground hits the ground. We substitute these values:
0 = -16t² + 176t
Solving the equation,
t = 0; t = 11 seconds
The rocket starts from the ground, t = 0, and comes back to the ground at t = 11 seconds.
h(t) will also equal 0 when the ground hits the ground. We substitute these values:
0 = -16t² + 176t
Solving the equation,
t = 0; t = 11 seconds
The rocket starts from the ground, t = 0, and comes back to the ground at t = 11 seconds.
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Final answer:
The rocket will hit the ground after 11 seconds.
Explanation:
To find the time it takes for the rocket to hit the ground, we can use the equation: h(t) = -16t² + v₀t + h₀. In this equation, h(t) represents the height of the rocket at time t, v₀ represents the initial vertical velocity, and h₀ represents the initial height. Since the rocket is launched from ground level, h₀ is equal to 0. We want to find the time when the rocket hits the ground, so we set h(t) equal to 0 and solve for t.
Plugging in the values, we have: -16t² + 176t = 0. Factoring out t, we have: t(-16t + 176) = 0. This equation yields two solutions: t = 0 and t = 11, but we discard t = 0 since it represents the time before the rocket is launched. Therefore, the rocket will hit the ground after 11 seconds.
