Posted by admin on Monday, September 29, 2008 · Leave a Comment
You are watching your friend play hockey. In the course of the game, he strikes the puck in such a way that, when it is at its highest point, it just clears the surrounding 2.86 m high Plexiglas wall that is 11.4 m away. (Ignore any effects due to air resistance.)
could you please show me how its done too.
thanks a lot
Let the initial velocity of puck is u m/s and the angle with horizon is A.
The Range (R) = u^2sin2A/g
=> 2 x 11.4 x 9.8 = u^2 sin2A
=>2u^2sinAcosA = 2 x 11.4 x 9.8
=>u^2sinAcosA = 11.4 x 9.8 = 111.72 -----------------------------(i)
Again Max. Height(H) = u^2sin^2A/2g
=>2.86 = u^2sin^2A/(2 x 9.8)
=>u^2sin^2 A = 2.86 x 2 x 9.8
=>u^2sin^2 A = 56.06 -------------------------------------------------(ii)
By (ii)/(i) =>tanA = 56.06/111.72 = 0.50 = tan 27*
=>A = 27*
by putting the value of A in (ii)
=> u^2 x (sin27*)^2 = 56.06
=>u^2 x(0.45)^2 = 56.06
=>u^2 = 56.06/0.20 =280.30
=>u = sqrt280.30 =16.74
Ans:-
(a) verticle component = u sinA = 16.74 x sin27* = 16.74 x 0.45 = 7.5 m/s
(b) time to reach the wall = usinA/g = 7.5/9.8 = 0.77 sec
(c) horizontal component = u cosA = 16.74 x cos27* = 16.74 x 0.89 = 14.92 m/s;
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