During a training exercise, a signaling flare is launched vertically upward from ground le… — Armed Services Vocational Aptitude Battery (ASVAB)

During a training exercise, a signaling flare is launched vertically upward from ground level with an initial velocity of $30\text{ m/s}$ . Assuming air resistance is negligible and using the approximation $g = 10\text{ m/s}^2$ , how many seconds will it take for the flare to reach its maximum height?

Answer: 3 s

Answer

It will take 3 seconds for the flare to reach its maximum height.

At its maximum height, any vertically launched object momentarily stops before falling back down, meaning its instantaneous velocity is

0\text{ m/s}

. Given an initial upward velocity of

30\text{ m/s}

, gravity decreases this velocity by

10\text{ m/s}

for every passing second. Therefore, it takes exactly 3 seconds for gravity to completely counteract the initial upward speed (

30 / 10 = 3

Step-by-Step Solution

Identify known variables and the final goal

v_i = 30\text{ m/s}

v_f = 0\text{ m/s}

(velocity is zero at the apex), and

a = -10\text{ m/s}^2

. The goal is to find time (

t

Establishing the initial and final states is required to choose the correct kinematic equation for free fall.

Select the appropriate kinematic formula

Use the equation

v_f = v_i + at

This formula connects initial velocity, final velocity, acceleration, and time, without needing to know the distance traveled.

Substitute the values and solve for

t

0 = 30 - 10t \Rightarrow 10t = 30 \Rightarrow t = 3

Solving the linear algebraic equation yields the exact time it takes for gravity to decelerate the flare to a stop.

Key Concept

Calculating the time to reach the apex of vertical projectile motion under uniform gravitational acceleration.

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