SOLUTION: You launch a rocket into the air with an initial upward velocity of 60ft/sec. starting at a height of 3ft.
How long until it hits the ground?
what was the maximum height of the
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Question 620999: You launch a rocket into the air with an initial upward velocity of 60ft/sec. starting at a height of 3ft.
How long until it hits the ground?
what was the maximum height of the rocket?
after how long did the maximum height occur?
at what two times was the rocket 50ft in the air?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The height of a projectile at time 
is given by the function
\ =\ \frac{1}{2}gt^2\ +\ v_ot\ +\ h_o)
Where 
is the acceleration due to gravity near the surface of whatever planet you are on. 
if you are still on Earth. 
is the initial upward velocity in feet per second, and 
is the initial height in feet.
The ground is height zero. Set the function equal to zero and solve for . Use the quadratic formula. Discard the negative root.
Since acceleration due to gravity is a negative quantity with respect to the initial direction of the rocket, the graph of the function is a parabola opening downward. Hence the vertex of the parabola is at the point \right))
, where 
represents the time that the vertex is obtained and )
is the maximum height obtained. Recall that the vertex of the parabola \ =\ ax^2\ +\ bx\ +\ c)
has an 
-coordinate of 
Set the function equal to 50 and solve the quadratic for . Use the quadratic formula.
John
My calculator said it, I believe it, that settles it
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