Chapter 10.7, Problem 52AYU

To determine

To find:

a. Parametric equations that model the motions of the bus and Jodi as a function of time. [Hint: The position s at time $t$ of an object having acceleration as is $s=1/2at²$].

Answer to Problem 52AYU

a. $\left(1.5t², 1\right)$, $\left(5\left(t - 2\right), 5\right)$

Explanation of Solution

Given:

Jodi’s bus leaves at 5:30 pm and accelerates at the rate of 3 meters per second per second. Jodi, who can run 5 meters per second, arrives at the bus station 2 seconds after the bus has left and runs for the bus.

Formula used:

$s = \frac{1}{2}at²$

Calculation:

Let $y_1 = 1$ be bus’s path and $y_2 = 5$ be Jodi’s path.

a. Bus: $x_1 = \frac{1}{2}\left(3\right)t² = 1.5t²$

$y_1 = 1$

Jodi:

$x_2 = 5\left(t - 2\right)$

$y_2 = 5$

To determine

To find:

b. Algebraically whether Jodi will catch the bus. If so, when?

Answer to Problem 52AYU

b. No, Jodi cannot catch the bus.

Explanation of Solution

Given:

Jodi’s bus leaves at 5:30 pm and accelerates at the rate of 3 meters per second per second. Jodi, who can run 5 meters per second, arrives at the bus station 2 seconds after the bus has left and runs for the bus.

Formula used:

$s = \frac{1}{2}at²$

Calculation:

Let $y_1 = 1$ be bus’s path and $y_2 = 5$ be Jodi’s path.

b.Bill will catch the train only when $x_1 = x_2$

$1.5t² = 5\left(t - 2\right)$

$1.5t² - 5t + 10 = 0$

$t$ does not have any real function as $b² - 4ac = 25 - 4 \&*\#x00A0;10 \&*\#x00A0;1.5 = -35 < 0$

Hence Jodi cannot catch the Bus.

To determine

To find:

c. Simulate the motion of the bus and Jodi by simultaneously graphing the equations found in part (a).

Answer to Problem 52AYU

c.

Explanation of Solution

Given:

Jodi’s bus leaves at 5:30 pm and accelerates at the rate of 3 meters per second per second. Jodi, who can run 5 meters per second, arrives at the bus station 2 seconds after the bus has left and runs for the bus.

Formula used:

$s = \frac{1}{2}at²$

Calculation:

Let $y_1 = 1$ be bus’s path and $y_2 = 5$ be Jodi’s path.

c.