a model rocket is launched straight upward at 58.8 m/s, how long does it take for the rocket to reach its peak height?

It takes the rocket 5.99 seconds to reach its peak.

Explanation:

From newton's equation of motion,

When the rocket is at its peak,

v = 0 m/s, acceleration due to gravity (g) = Negative.

Using

g = v-u/t ... Equation 1

Where g = acceleration due to gravity, v = final velocity, u = initial velocity, t = time.

Making t the subject of the equation.

t = (v-u) / g ... Equation 2.

Given: v = 0 m/s, u = 58.8 m/s, g = - 9.81 m/s²

Substituting into equation 2

t = (0-58.8) / -9.81

t = - 58.8/-9.81

t = 5.99 seconds.

Thus it takes the rocket 5.99 seconds to reach its peak.