Chapter 3, Problem 7E

A ball is thrown upward with an initial velocity of 13 m/s. Using the approximate value of g = 10 m/s², what are the magnitude and direction of the ball’s velocity:

1. a. 1 second after it is thrown?
2. b. 2 seconds after it is thrown?

To determine

The magnitude and direction of the velocity of the ball $1\text{s}$ after it is thrown.

Answer to Problem 7E

The velocity of the ball is $3\text{m/s}$ in the upward direction.

Explanation of Solution

Given Info: A ball is thrown upward with initial velocity $13\text{m/s}$. The value of $g$ is $10{\text{m/s}}^2$.

Write the expression for the final velocity.

$v=u-gt$

Here,

$v$ is the final velocity

$u$ is the initial velocity

$g$ is the acceleration due to gravity

$t$ is the time

Substitute $13\text{m/s}$ for $u$, $10{\text{m/s}}^2$ for $g$ and $1\text{s}$ for $t$ to get $v$.

$\begin{array}{c}v=13\text{m/s}-\left(10{\text{m/s}}^2\right)\left(1\text{s}\right)\\ =+3\text{m/s}\end{array}$

The positive sign indicates the motion is in the upward direction.

Conclusion:

Thus, the velocity of the ball is $3\text{m/s}$ in the upward direction.

To determine

The magnitude and direction of the velocity of the ball $2\text{s}$ after it is thrown.

Answer to Problem 7E

The velocity of the ball is $7\text{m/s}$ in the downward direction.

Explanation of Solution

Given Info: A ball is thrown upward with initial velocity $13\text{m/s}$. The value of $g$ is $10{\text{m/s}}^2$.

Write the expression for the final velocity.

$v=u-gt$

Substitute $13\text{m/s}$ for $u$, $10{\text{m/s}}^2$ for $g$ and $2\text{s}$ for $t$ to get $v$.

$\begin{array}{c}v=13\text{m/s}-\left(10{\text{m/s}}^2\right)\left(2\text{s}\right)\\ =-7\text{m/s}\end{array}$

The negative sign indicates the motion is in the downward direction.

Conclusion:

Thus, the velocity of the ball is $7\text{m/s}$ in the downward direction.