After finding the keys to the Batmobile lying on the pavement, The Joker and The

Question

After finding the keys to the Batmobile lying on the pavement, The Joker and The Riddler decide to play a game of keep-away with Batman. The Joker and The Riddler toss the keys to each other over Batman's head, as depicted below. Having enough of this, Batman decides to use his grappling hook to catch the keys while they are in mid-air. Exactly when the Joker throws the keys, Batman will fire his grappling hook directly upwards. If the Joker throws the keys at 10 m/s at a 60 degree angle above the horizontal, and Batman is 3 m away from the Joker, what initial speed does the grappling hook need to have for it to catch the keys? (Assume that the grappling hook and keys are thrown from the same initial height above the ground).

Explanation / Answer

let us know that if we through key from joker than time travel to rise = equal to time travel by horizonatl component of key velocity

time t=3/10cos60=0.6 sec

now distance travel by horizonatal component

h=ut-0.5gt2=10sin60*.6 -0.5*9.8*0.62=3.4321 m

but again calculatin of initial velocity of gripp throw by batman

3.4321=u*0.6-0.5*9.8*0.62

u=8.66m/s of batman hook

we did it watse calculation for same time staring we have to find vertical component of key velocity because we have to reach same time same postion so velocity will be same=8.66m/s

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