A particle moves along the x-axis so that its velocity at anytime is t greater than or equal to 0 is given by v(t)=1-sin(2pi t)
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Answer:
The net should be placed at a height of 8.45 m
Explanation:
In order to calculate the height you have to apply the equations of <em>projectil motion.</em>
For x-axis, the position at a time t is given by:
Xf=Xo +(VoCosα)t (I)
Where Xf is the final position, Xo is the initial position, Vo is the initial speed and t is the time.
For the y-axis, the position at a time t is given by:
Yf=Yo + (VoSinα)t - 0.5g (II)
Where Yf is the final position, Yo is the initial position, Vo is the initial speed, t is the time and g is the acceleration of gravity.
For both equations, ∝ is the angle formed by the cannon and the horizontal
The height where the net should be placed in order to catch the daredevil is given by replacing the time when the daredevil will be in the horizontal position of 39.7 m in the equation of position for the y-axis.
So, you have to calculate the time using (I)
Let the system of reference be placed at x=o and y=o
Xf= 0 + 25.9Cos(31,4◦)t
Xf=39.7
39.7=22.1t
Dividing both sides by 22.1 to find the value of t:
t=1.79 seconds
Replacing the time in equation (II) to find the height:
Yf=0 +25.9Sin(31,4◦)(1.79) - 0.5(9.8)
Yf= 8.45 m
So the height is 8.45 m