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Velocity along x-axis = ux = u cos θ
Acceleration along x-axis ax = 0
Velocity along y-axis = uy = u sin θ
Acceleration along y-axis ay = -g
Here we use different equation of motions of one dimension derived earlier to get the different parameters.
…... (a)
…... (b)
v2 = v02 – 2g (y-y0) …... (c)
When body returns to the same horizontal level, the resultant displacement in vertical y-direction is zero. Use equation b.
Therefore, 0 = (u sin θ) t - (½)gt2,
As t cannot equal to zero, then, total time of flight,
Horizontal Range (OA=X) = Horizontal velocity × Time of flight
= u cos θ × 2 u sin θ/g
So horizontal range,
At the highest point of the trajectory, vertical component of velocity is zero.
Therefore, 0 = (u sin θ)2 - 2g Hmax
So, maximum height would be,
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