Find the verticaland horizontal components of the launch velocity. Decide: durin

Question

Find the verticaland horizontal components of the launch velocity. Decide: duringthe stone's flight, what is the vertical component of acceleration?The horizontal component of acceleration? The vertical motion andhorizontal motions can be treated independently and with theconstant-acceleration equations of Chapter 2, as rewritten inChapter 4.
The speed just before impact is the magnitude of the velocityvector just then, which can be determined from the velocitycomponents using the Pythagorean Theorem.
Section 4-6 Projectile MotionAnalyzed

Explanation / Answer

Probably easiest to solve for H first. sin 60 = vy/41 vy = 41 * sin 60 =35.51 m/s v = v0 -gt, we're solving for when v= 0, sogt=V0=35.51 solving for for t, we get t=3.62 s. To find H, we set H = (1/2)(V+V0)t=(1/2)(35.51)(3.62)=64.27m We know that the entire problem happens in the span of 5.8 s, solet's find how far the stone will be launched horizontally beforestopping. 41 * cos 60 = 20.5 m/s There is no horizontal resistance, so x=v0t= 20.5*5.8=118.9 m The halfway point of the arc is at t=3.62, sox=v0t=20.5*3.62 = 74.21 m So we know that the stone moved another 44.69 feet horizontallybefore stopping. We also know that when the stone hadtravelled 29.52 feet, it was going the same speed (differentdirection) as it was right before striking the elevatedground. Now, if we see how long it takes the stone to go29.52 feet... 29.52=20.5t t=1.44 s Knowing this, we can find h and the speed before impact. v=v0-gt v=20.5-9.81*1.44 v=6.3736 m/s in the vertical direction. Using the pythagorean theorum, we can find the overallvelocity. 6.37362+20.52=21.47m/s. The stone was travelling at 21.47 m/s when it impactedat point A. From here, we can find h by using h =v0t-(1/2)(g)t2, where t = 1.44 s. Solving for h, we finally find that h=19.36 m

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