Question

fill out the g, u, and e for each of the following problems: sub and solve together
a baseball is thrown horizontally at 45 m/s. the ball slows down at a rate of -5 m/s2. how long is the ball in the air before coming to rest?
g vi = 45 a=-5 vf = 0
u t =?
e
s.s
motion diagram
an airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until finally lifts off the ground. determine the distance traveled before take - off.
g
u
e
s.s
motion diagram

Explanation:

Step1: Identify the kinematic - equation

We use the equation $v = v_0+at$, where $v$ is final velocity, $v_0$ is initial velocity, $a$ is acceleration and $t$ is time.

Step2: Rearrange the equation for time

From $v = v_0+at$, we can solve for $t$ as $t=\frac{v - v_0}{a}$.

Step3: Substitute the values

Given $v_0 = 45\ m/s$, $v = 0\ m/s$ and $a=- 5\ m/s^2$. Then $t=\frac{0 - 45}{-5}$.

Step4: Calculate the time

$t=\frac{-45}{-5}=9\ s$.

for second - problem:

Step1: Identify the kinematic - equation

We use the equation $x=v_0t+\frac{1}{2}at^{2}$. Since the airplane starts from rest, $v_0 = 0\ m/s$. So the equation simplifies to $x=\frac{1}{2}at^{2}$.

Step2: Substitute the values

Given $a = 3.20\ m/s^{2}$ and $t = 32.8\ s$. Then $x=\frac{1}{2}\times3.20\times(32.8)^{2}$.

Step3: Calculate the distance

First, $(32.8)^{2}=1075.84$. Then $\frac{1}{2}\times3.20\times1075.84 = 1.6\times1075.84=1721.344\ m$.

Answer:

9 s