# Jump Across Stream#

A very bored 313 $$kg$$ bear decided to jump across a stream. The stream is 4.2 $$m$$ wide and the east bank of the stream is 1.1 $$\rm{m}$$ higher than the west bank (where the bear starts). The bear can jump with an initial velocity $$\overrightarrow{V_i} =$$ 3$$\rm{m\over s}\hat{\imath}+$$ 4 $$\rm{m\over s}\hat{\jmath}$$, and decides to start from 3.1 $$\rm{m}$$ in the air, halfway up a sturdy tree.

## Part 1#

If the origin is at the bear’s foot (up in the tree), write an equation describing the $$x$$ coordinate of the bear while it is in the air.

Use the following table as a reference. Note that it may not be necessary to use every variable.

For

Use

$$\Delta t$$

t

$$g$$

g

## Part 2#

If the origin is at the bear’s foot (up in the tree), write an equation describing the $$y$$ coordinate of the bear while it is in the air.

Use the following table as a reference. Note that it may not be necessary to use every variable.

For

Use

$$\Delta t$$

t

$$g$$

g

## Part 3#

If the origin is at the bear’s foot (up in the tree), write an equation describing the $$V_x$$ component of the velocity of the bear while it is in the air.

Use the following table as a reference. Note that it may not be necessary to use every variable.

For

Use

$$\Delta t$$

t

$$g$$

g

## Part 4#

If the origin is at the foot of the bear’s jumping tree, write an equation describing the $$V_y$$ component of the velocity of the bear while it is in the air.

Use the following table as a reference. Note that it may not be necessary to use every variable.

For

Use

$$\Delta t$$

t

$$g$$

g

## Part 5#

Does the bear make it to the other side of the stream?

• Yes, the bear makes it to the other side of the stream.

• No, the bear does not make it to the other side of the stream.

## Part 6#

When the bear is at its highest ($$y$$ or vertical) position above the stream, what is the $$x$$-coordinate of the bear?

Please enter in a numeric value in m.

## Part 7#

Where is the $$y$$-coordinate of the bear’s highest position above the stream?

Please enter in a numeric value in m.

## Part 8#

What is the bear’s velocity when it reaches its maximum height?

Use the following table as a reference.

For

Use

$$\hat{\imath}$$

i_hat

$$\hat{\jmath}$$

j_hat

## Part 9#

This question is much easier to do in the frame of an observer moving with velocity $$\vec{u} =$$ 3 $$\rm{m\over s}\hat{\imath} +$$ 0 $$\rm{m\over s}\hat{\jmath}$$. Describe why?

• The problem would become a 1-D problem with motion only in the $$y$$-direction.
• The problem would become a 1-D problem with motion only in the $$x$$-direction.