Question

Oliver

and
Harry
take
part
in
running
competitions.
Oliver's
mass
is
half
the
mass
of
Harry
and
Oliver's
speed
is
2
times
greater
than
that
of
Harry.
By
how
much
must
Harry
speed
up
if
he
wants
to
have
the
same
kinetic
energy
as
Oliver?
Harry's
original
speed
is
6m/s
Give
your
answer
to
2
decimal
places.

Answer 1

Harry must speed up to approximately 8.49 m/s to have the same kinetic energy as Oliver, whose speed is twice that of Harry.

To find how much Harry must speed up to have the same kinetic energy as Oliver, we'll use the kinetic energy equation
`\(KE = (1)/(2)mv^2\)`, where m is mass and v is speed.

Let
`\(m_O\) and \(v_O\)` be Oliver's mass and speed, and
`\(m_H\) and \(v_H\)` be Harry's mass and speed.

Given
`\(m_O = (1)/(2)m_H\) and \(v_O = 2v_H\)`, the kinetic energy of Oliver (
`\(KE_O\)`) can be expressed as:

`\[ KE_O = (1)/(2) m_O v_O^2 \]`

Substitute the given values:

`\[ KE_O = (1)/(2) \left((1)/(2) m_H\right) (2v_H)^2 \]`

Simplify:

`\[ KE_O = (1)/(2) \cdot (1)/(2) m_H \cdot 4v_H^2 \]`

`\[ KE_O = m_H v_H^2 \]`

Now, set Oliver's kinetic energy equal to Harry's kinetic energy:

`\[ m_H v_H^2 = (1)/(2) m_H (v_H')^2 \]`

Solve for
`\(v_H'\)` (the speed Harry needs to achieve):

`\[ v_H' = √(2) \cdot v_H \]`

Given that Harry's original speed (
`\(v_H\)`) is 6 m/s, the new speed (
`\(v_H'\)`) is:

`\[ v_H' = √(2) \cdot 6 \approx 8.49 \, \text{m/s} \]`