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Grade: 12th pass
        
A dartboard is 3.0 m away. A dart is thrown horizontally from height 1.90 m hits the board at 1.60 m.Calculate the                (a) time of flight.                                                                         (b) intial speed of the dart.                                                       © speed of the dart when its hits the board.
one month ago

Answers : (1)

Arun
22824 Points
							
when you throw a ball in the horizontal direction, don't you see it hitting the ground after sometime? it is true that the horizontal speed remains constant but as soon as you release it, the vertical component of velocity which is initially 0m/s increases due to the action of gravity.so here is the working.
a)initial vertical velocity(uy)=0m/s
height through which it falls(h)=0.3m
from 2nd equation of motion(h=uy+gt^2)[g=10m/s^2]
we get,
h=1/2(10)t^2=>t=0.24s
b) horizontal speed(ux) remains constant also range(R)=3m
t=0.24s
from R=ux(t)
we get,
ux=12.5m/s.
c)just before striking the board, the dart now has a vertical component of velocity since it accelerates under the influence of gravity and the horizontal component which remains constant throughout the journey(ux=vx). Their resultant will give you the answer.
so,
vertical velocity attained by the dart(vy) is given by
vy=uy+gt
on substituting and solving
we get,
vy=2.4m/s[uy=0]
resultant(V)given by squareroot(vy^2+vx^2)=>V = 12.72 m/sec
one month ago
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