Questions: A soccer ball is kicked vertically into the air with an initial velocity of 17.3 m / s. How long will it take for the ball to reach its highest point? Hint: vf=vi+a * t

A soccer ball is kicked vertically into the air with an initial velocity of 17.3 m / s. How long will it take for the ball to reach its highest point?

Hint: vf=vi+a * t

Transcript text: A soccer ball is kicked vertically into the air with an initial velocity of $17.3 \mathrm{~m} / \mathrm{s}$. How long will it take for the ball to reach its highest point? Hint: $v_{f}=v_{i}+a * t$

Solution

Solution Steps

Step 1: Understand the Problem

We need to determine the time it takes for a soccer ball, kicked vertically with an initial velocity of $17.3 \, \text{m/s}$, to reach its highest point. At the highest point, the final velocity ($v_f$) of the ball will be $0 \, \text{m/s}$.

Step 2: Use the Kinematic Equation

The kinematic equation that relates initial velocity ($v_i$), final velocity ($v_f$), acceleration ($a$), and time ($t$) is: \[ v_f = v_i + a \cdot t \] In this scenario:

$v_f = 0 \, \text{m/s}$ (at the highest point)
$v_i = 17.3 \, \text{m/s}$
$a = -9.81 \, \text{m/s}^2$ (acceleration due to gravity, negative because it acts downward)

Step 3: Solve for Time

Rearrange the equation to solve for $t$: \[ 0 = 17.3 + (-9.81) \cdot t \] \[ -17.3 = -9.81 \cdot t \] \[ t = \frac{17.3}{9.81} \]

Step 4: Calculate the Time

Calculate the time using the values: \[ t = \frac{17.3}{9.81} \approx 1.7631 \, \text{s} \]