You are given the equations that are used to solve a problem. For each of these, you are to

a. Write a realistic problem for which these are the correct equations. Be sure that the answer your problem requests is consistent with the equations given.

b. Finish the solution of the problem, including a pictorial representation.

$$\begin{gathered} {\mathrm{v}}_{\mathrm{x}}=-(6\cos 45°)\mathrm{m}/\mathrm{s}+3\mathrm{m}/\mathrm{s} \\ {\mathrm{v}}_{\mathrm{y}}=6\sin 45°+0\mathrm{m}/\mathrm{s} \\ {\mathrm{v}}_{\mathrm{y}}{\mathrm{t}}_1=100\mathrm{m} \\ {\mathrm{x}}_1={\mathrm{v}}_{\mathrm{x}}{\mathrm{t}}_1 \end{gathered}$$

We are given with the equations:

a. We have to write a realistic problem for which these are the correct equations.

b. Finish the solution of the problem, including a pictorial representation.

A stone is thrown at an angle from a moving boat is$45°$. Initially the velocity is $6\mathrm{m}/\mathrm{s}$and the horizontal initial velocity is $3\mathrm{m}/\mathrm{s}$. Calculate the time and the distance traveled by the stone in water?

From first equation we get:

$$\begin{gathered} {\mathrm{v}}_{\mathrm{x}}=-(6\cos 45°)\mathrm{m}/\mathrm{s}+3\mathrm{m}/\mathrm{s} \\ {\mathrm{v}}_{\mathrm{x}}=-4.24\mathrm{m}/\mathrm{s}+3\mathrm{m}/\mathrm{s} \\ {\mathrm{v}}_{\mathrm{x}}=-1.24\mathrm{m}/\mathrm{s} \end{gathered}$$

From the second equation:

$$\begin{gathered} {\mathrm{v}}_{\mathrm{y}}=(6\sin 45°)\mathrm{m}/\mathrm{s}+0\mathrm{m}/\mathrm{s} \\ {\mathrm{v}}_{\mathrm{y}}=4.24\mathrm{m}/\mathrm{s} \end{gathered}$$

From third one:

$$\begin{gathered} {\mathrm{v}}_{\mathrm{y}}{\mathrm{t}}_1=100\mathrm{m} \\ 4.24\mathrm{m}/\mathrm{s}\times {\mathrm{t}}_1=100 \\ {\mathrm{t}}_1=23.57\mathrm{s} \end{gathered}$$

From last one equation:

localid="1648127870472" $$\begin{gathered} {\mathrm{x}}_1={\mathrm{v}}_{\mathrm{x}}{\mathrm{t}}_1 \\ {\mathrm{x}}_1=-1.24\mathrm{m}/\mathrm{s}\times 23.57\mathrm{s} \\ {\mathrm{x}}_1=-30\mathrm{m} \end{gathered}$$

Negative sign show that the car travels along west.

The Pictorial representation of the given equations are as: