Jump Across Stream#

A very bored 437 \(kg\) bear decided to jump across a stream. The stream is 2.3 \(m\) wide and the east bank of the stream is 1.3 \(\rm{m}\) higher than the west bank (where the bear starts). The bear can jump with an initial velocity \(\overrightarrow{V_i} = \) 2\(\rm{m\over s}\hat{\imath}+\) 2 \(\rm{m\over s}\hat{\jmath}\), and decides to start from 2.5 \(\rm{m}\) 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

Answer Section#

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

Answer Section#

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

Answer Section#

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

Answer Section#

Part 5#

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

Answer Section#

  • 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?

Answer Section#

Please enter in a numeric value in m.

Part 7#

Where is the \(y\)-coordinate of the bear’s highest position above the stream?

Answer Section#

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

Answer Section#

Part 9#

This question is much easier to do in the frame of an observer moving with velocity \(\vec{u} = \) 2 \(\rm{m\over s}\hat{\imath} + \) 0 \(\rm{m\over s}\hat{\jmath}\). Describe why?

Answer Section#

  • 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.

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.