ans:Final momentum of boat: px = 1732, py = 11,000. pf = 11136, vf = 11.36 m/sec
ID: 1388539 • Letter: A
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ans:Final momentum of boat: px = 1732, py = 11,000. pf = 11136, vf = 11.36 m/sec since mass = 980 kg. angle = 81o from x axis or 9o change from original course. How to do this problem?
T = 15567 N At pivot, Px = Tx = 13481 N Py = W + Wmm - Ty = 7517 N Stress at pivot = 15435 N Be careful to use the correct angles. Angle between wire and beam: 67 degree. T = 216.9 N At pivot, Px = TX = 187.8 N. (What is the correct angle to use to find Tx and Ty?) Py = 191.5 N Stress at pivot = 268.3 N A 100-kg boat (including the 20.kg cannonball) is moving initially at 10 m/sec in the direction shown. A 20-kg cannonball is fired in the direction shown at a speed of 100 m/sec. What is the velocity (speed and direction) of the ship immediately after firing?Explanation / Answer
Initial momentum of boat= 1000*10=10000kg-m/sec.
Let, Boat's final speed is v and it makes angle theta with Positive X-axis.
Since the initial momentum is along Y-direction,so the net final momentum will also be across Y-direction only.The momentum created in negative X-direction by the cannon(after firing) will be counterbalanced by the momentum of ship in positive X-direction.
So, 20*100*cos(30 degree)=980*v*cos(theta)
v*cos(theta)=1.767 -------1
Again,
Net Momentum along +ve Y-direction will remain unchanged.
So, 10000=(980*v*sin(theta))-(20*100*sin(30 degree))
v*sin(theta)=11.224 ------2
dividing 2 by 1,
Tan(theta)= 6.352
Theta= 81.05 degree from positive X- axis.
Putting this value of theta in 1, we get value of v.
v= 11.362 m/sec.
So, the boat's final speed will be 11.362m/sec and the angle with which it will move will be 81.05 degree from positive X- axis.
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