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A small toy rocket is launched from a 32-foot pad. The height ( h, in feet) of the rocket t seconds after taking off is given by the formula h=−2t2+0t+32 . How long will it take the rocket to hit the ground?t=______(Separate answers by a comma. Write answers as integers or reduced fractions.)

A small toy rocket is launched from a 32foot pad The height h in feet of the rocket t seconds after taking off is given by the formula h2t20t32 How long will it class=

Respuesta :

Given: A small toy rocket is launched from a 32-foot pad. The height (h, in feet) of the rocket t seconds after taking off is given by the formula

[tex]h=-2t^2+0t+32[/tex]

Required: To find out how long will it take the rocket to hit the ground.

Explanation: When the rocket touches the ground its height will be zero i.e.,

[tex]\begin{gathered} -2t^2+0t+32=0 \\ 2t^2=32 \\ t^2=16 \end{gathered}[/tex]

Which gives

[tex]t=\pm4[/tex]

Neglecting the negative value of t since time cannot be negative. We have

[tex]t=4\text{ seconds}[/tex]

Final Answer: Time, t=4 seconds.

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