A projectile is shot from the ground at an angle of pi/6 and a speed of 25 m/s. Factoring in both horizontal and vertical movement, what will the projectile's distance from the starting point be when it reaches its maximum height?

1 Answer
Apr 15, 2016

~~31.2m

Explanation:

The velocity of projection of the projectile u=25ms^-1
The angle of projection of the projectile alpha=pi/6
The horizontal component of velocity of projection
u_h=ucosalpha=25xxcos(pi/6)=12.5sqrt3ms^-1
TheVertical component of velocity of projection
u_v=ucosalpha=25xxsin(pi/6)=12.5ms^-1


Assuming the ideal situation where gravitational pull is the only force acting on the body and no air resistance exists , we can easily proceed for various calculation using equation of motion under gravity.
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CALCULATION
Let the projectile reaches its maximum height H m after t s of its start.
The final vertical component of its velocity at maximum height will be zero
So we can write
0 = usinalpha-gxxt =>t = (usinalpha)/g=12.5/10=1.25s taking g=10ms^-2

Again
0^2=(usinalpha)^2-2xxgxxH
=>H = (usinalpha)^2/g=(12.5)^2/10=15.625m

During t=1.25s of its ascent its horizontal component will remain unaltered and that is why the horizontal displacement
R = ucosalpha xxt=12.5sqrt3xx1.25m=27m

Hence the projectil's distance ( D ) from starting point to the maximum point of its ascent is given by
D=sqrt(R^2+H^2)=sqrt(27^2+(15.625)^2)~~31.2m

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