Stoned and stoner: While standing on a bridge 15.0 m above the river, you drop a

Question

Stoned and stoner: While standing on a bridge 15.0 m above the river, you drop a stone from rest. When the stone has fallen 3.20 m, you throw a second stone straight down. What initial velocity must you give the second stone if they are both to splash at the same instant? Eh ... What's up, doc? Coyote is hungry and from its observation point on the ledge of a 50 m cliff, it spots Bugs Bunny snoozing in a bed of carrot leaves at the base of the cliff Coyote drops a boulder, sure of getting a juicy meal. But the swooshing sound of the falling weapon awakes Bugs at the moment the boulder is 14 m above its head. How much time does Bugs have to get out of the way?

Explanation / Answer

Distance 'S' travelled in a time 't' is given by

S=ut+(1/2)a*t2

where u is initial velocity

a is acceleration due to gravity

Time taken for stone 1 to reach 3.2m

3.2=0*t+(1/2)*9.8*t2

solving for t, t1=0.808 sec

time that will be taken for stone 1 to travel 15m is

15=0*t+(1/2)*9.8*t2

15=(1/2)*9.8t2

solving for t, t2 = 1.75

Time that should be taken by stone 2 to reach water the same time as stone 1 is

t2 -t1 = 1.75 - 0.808

= 0.942 sec

So for stone 2 to travel 15m in 0.942s we must throw it at velocity u,

lets calculate u

S=ut+(1/2)a*t2

15 = u*0.942+(1/2)*9.8*(0.942)2

10.65 = u*0.942

u = 11.307 m/s

we must give a velocity of 11.307m/s

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