Question

A rocket was launched and its height, h, in metres, above the ground after time,

t, in seconds, is represented by h = 11 + 10t - 2².For how many seconds was
the rocket in the air?
a) about 6.64 s
b) about 6.27 s
c) about 5.93 s
d) about 7.35 s

Answer 1

The rocket was in the air for approximately 3.79 seconds.

The rocket's time in the air can be determined by solving the quadratic equation 0 = 11 + 10t - t². Using the quadratic formula, the solution t = 3.79 s represents the time the rocket is in the air, making the correct answer approximately 3.79 seconds, with a possible typographical error in the choices provided.

Step-by-step explanation:

The rocket's height above the ground is given by the equation h = 11 + 10t - 2t^2. To find out how long the rocket was in the air, we need to determine the time when the rocket hits the ground. This can be done by setting h = 0 and solving for t. The quadratic formula can be used to solve the equation for t, and it yields two solutions: t = 3.79 s and t = 0.54 s. Since the rocket starts from the ground and lands back on the ground, we take the longer solution, t = 3.79 s, as the time the rocket was in the air.