what vertical velocity is necessary for the keys to just reach your friend's hand 6m above the ground?
Suppose you want to throw some keys to a friend standing on a second-floor balcony. if you release the keys at 1.5m above the ground, what vertical velocity is necessary for the keys to just reach your friend's hand 6m above the ground?
Useful Equation: a=dv/dt=dv/ds(ds/dt)=(dv/ds)(v)
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Verified answer
Given
Friend 6m
You 1.5m
Final Velocity is given by
vf = v + g*t
where
vf is final velocity
v is initial velocity
When it reaches the highest point
0 = v - gt
t = v/g
Distance with gravity is given by
d = v*t - (1/2)gt^2
where d is the (vertical) distance
6 - 1.5 = v*(v/g) - (1/2)g(v/g)^2
4.5 = v^2/g - (1/2)v^2/g
= v^2/(2g)
v = ± √ ̅(4.5*2*9.8)
= 9.39
Answer: the velocity of 9.39 m/s is needed.