Peoples Physics Book Version-2

http://www.ck12.org Chapter 5. Two Dimensional and Projectile Motion Version 2

5.4 Two Dimensional Example

Example 1

Question: A ball of massmis moving horizontally with a speed ofvioff a cliff of heighth. How much time does it

take the ball to travel from the edge of the cliff to the ground? Express your answer in terms ofg(acceleration due

to gravity) andh(height of the cliff).

Solution: Since we are solving for the time, any motion in thexdirection is not pertinent. We can just use the

equation

f=~v

i + t
~v

f=_i + t

and solve for t. Notice though thatviy, the ball’s initial velocity in theydirection, is equal to zero when the ball rolls

of the cliff. We can therefore disregard it; we have:

vyf=ayt

Therefore,

t=

vyf

a

Though we have solved fort, we have not solved for it in terms of the given quantities We can replaceawithg

because the only acceleration on the ball is due to gravity. We now need to replacevyfwith some combination ofh

andg. Using the equation

fv

^2=v_i^2+2ax,

we can solve forv

f^2inthetermswanted.Notethatxheredenotesthedistancetraveledbytheob ject,orh.Itisn′tthehorizontalx.Because

v_yi^2=0,wecanonceagaindisregardit.Wenowre placexwithhandawithg.T hisgivesusBecausewehavesolved f or

v_f^2wewillmaketheotherequation−−−theonesolved f ort−−−alsocontainv_f^2.S peci f ically,Nowwecansubstitute

2ghf orv_f^2.Wecanthensolve f ortheanswer: