Question

The height of a rocket launched upward from a 160 foot cliff is modeled by

h = -16t^2+48t+160, where h is the height in feet and t is the seconds. feet and t is the time in seconds. How many seconds was the rocket in the air?
the rocket was in the air for____ seconds.

Answer 1

The quadratic equation h = -16t^2 + 48t + 160 models the rocket's height over time. By setting h to zero and solving the equation, we find that the rocket was in the air for 5 seconds.

Step-by-step explanation:

To determine how many seconds the rocket was in the air, we need to find when the height (h) of the rocket is equal to zero after launch. The height of a rocket launched from a 160-foot cliff is modeled by the equation h = -16t2 + 48t + 160. To find the time when the rocket hits the ground (h=0), we solve for t using this equation:

• Set the quadratic equation equal to zero: 0 = -16t2 + 48t + 160.
• Divide the entire equation by -16 to simplify: 0 = t2 - 3t - 10.
• Factor the quadratic: (t - 5)(t + 2) = 0.
• Find the positive root since time cannot be negative: t = 5 seconds.

Therefore, the rocket was in the air for 5 seconds.