A rocket is launched straight up into the air with an initial velocity of 23.5 m/s. How much time does it take for the rocket to reach its maximum height?

To determine the time it takes for the rocket to reach its maximum height, we can use the following kinematic equation: \[ v = u + at \] where: - \( v \) = final velocity (0 m/s at the maximum height), - \( u \) = initial velocity (23.5 m/s), - \( a \) = acceleration (which will be \(-9.81 \, \text{m/s}^2\) due to gravity acting downward), - \( t \) = time (what we want to find). At maximum height, the final velocity \( v \) is 0, so we set up the equation: \[ 0 = 23.5 \, \text{m/s} - 9.81 \, \text{m/s}^2 \cdot t \] Rearranging gives: \[ 9.81 \, \text{m/s}^2 \cdot t = 23.5 \, \text{m/s} \] Now, solve for \( t \): \[ t = \frac{23.5 \, \text{m/s}}{9.81 \, \text{m/s}^2} \] Calculating this: \[ t \approx \frac{23.5}{9.81} \approx 2.39 \, \text{s} \] Therefore, it takes approximately **2.39 seconds** for the rocket to reach its maximum height.