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Answer :
Final answer:
To find the time it takes for the toy rocket to return to the ground, we set the height equation to zero and solve for t. The quadratic equation -16t^2 + 135t = 0 has two solutions: t = 0 (launch time) and t = 135/16, which equals approximately 8.44 seconds, the time of flight until the rocket returns to the ground.
Explanation:
When the toy rocket is launched vertically upward from ground level with an initial velocity of 135 feet per second, and its height h after t seconds is given by the equation h(t) = -16t2 + 135t, we want to find the time it takes for the rocket to return to the ground. Returning to the ground means that the height h will be 0. We can solve this by setting the equation equal to 0 and solving for t:
0 = -16t2 + 135t
This is a quadratic equation, which we can solve by factoring or using the quadratic formula. In this case, factoring is possible:
0 = t(-16t + 135)
The solutions to this equation are t = 0, which is the time of launch, and t = 135/16, which is the time of flight until the rocket returns to the ground. We divide 135 by 16 to find:
t = 8.4375 seconds
The rocket will take approximately 8.44 seconds to return to the ground.
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Answer:
The toy rocket will return to the ground at 8.44 seconds
Step-by-step explanation:
The height h of the toy rocket launched vertically as a function of the time t is given by:
[tex]h(t)=-16t^2+135t[/tex]
The rocket will return to the ground when h=0:
[tex]-16t^2+135t=0[/tex]
Factoring:
[tex]t(-16t+135)=0[/tex]
There are two solutions:
t=0, t = 135/16 = 8.4375
The first solution corresponds to the moment the toy rocket was launched, the second is the time taken by the rocket to return to the ground.
The toy rocket will return to the ground at 8.44 seconds
