- #1

Hemingway

- 42

- 0

## Homework Statement

A motorcyclist is trying to leap across a canyon. The first cliff is 70m high, she wants to jump to the cliff 35m high. She is traveling 38m/s. Ignoring air resistance, find the speed with which the cycle strikes the ground on the other side.

I think (and am very worried by this) that my algebra is incorrect as I do not get the same answer as the textbook which is v = 46.2m/s

## Homework Equations

1/2mv

^{2}+ mgh

_{f}= 1/2mv

_{0}

^{2}+mgh

_{0}

## The Attempt at a Solution

1/2mv

^{2}+ mgh

_{f}= 1/2mv

_{0}

^{2}+mgh

_{0}

v

^{2}+ gh

_{f}= u

^{2}+ gh

_{0}

v

^{2}+ (9.8) (35) = 38

^{2}+ 9.8 (70)

v

^{2}= 1444 + 686 (-343)

v

^{2}= 1787

v = 42.3m/s

I know the equation is incorrectly reduced. The textbook has

(1) 1/2mv

^{2}+ mgh

_{f}= 1/2mv

_{0}

^{2}+mgh

_{0}

to:

(2) vf = √(v

_{0}

^{2}+ 2g (h

_{0}- h

_{f})

I'm worried because it might mean I'm having a problem with fundementals - I would have just forgotten I used to be great at this stuff.

I have basically two questions:

- Is the final equation (2) not from (1) but just a form of the kinematics equation - so (1) cannot be reduced to (2)

- or what algebraic thing am I doing wrong? I cannot see how 2g happens as (1/2) / (1/2) = 1... I can't see what I can do to get 2g from equation 1.

Thanks as always to this forum!