Tough Projectile Motion Problem - Physics?

Question

Solve the initial velocity of a projectile being fired at an Angle of 9 degrees above the horizontal. It is fired from 1.015m above where it lands, and displacement in the x direction is 3.885m.

What is the initial velocity?

Answer 1

Draw a right triangle. The velocity, v, is the hypotenuse. The velocity in the x direction, vx, is the bottom leg. The velocity in the y direction, vy, is the vertical leg. From this, we get a few definitions....

If θ is the base angle of the right triangle, then

vx = v cos θ
vy = v sin θ

The good thing here, is that θ = 10º.

We first need to determine the time it took for the object to fall 1.015 m with the given conditions. This is tough, since we don't know vy. Instead of vy, however, let's use v sin θ and see what we get.

y = ½ g t² + v sin θ t + h

y = 0 (the final height)
g = -9.8 (acceleration due to gravity)
v = we don't know yet
t = time
h = 1.015 (initial height)

0 = ½(-9.8)t² + v sin 9º t + 1.015
0 = -4.9t² + 0.156 v t + 1.015

Using the quadratic formula to solve for t, we get

t = 0.0159 ( sqrt(v² + 817.5) + v)

I know it's ugly, but it's necessary.
Now, we know there's no acceleration in the x direction, so

x = vx t = v cos θ t

3.885 = v cos 9º (0.0159 ( sqrt(v² + 817.5) + v))

All we have to do now is solve this monster of an equation for v. You were right when you said it was tough :)

Solving for v, you get

v = 6.82276 m/s

about 6.823 m/s

Answer 2

Air resistance certainly can result projectile action, even with the undeniable fact that that's many times assumed to be negligible in physics training so as that the simplest formula can study and understood. the 1st results of air resistance would be to sluggish the projectile because it travels. this would turn an arc path to a parabolic path. the 2nd results of air resistance would be to account for wind which might push the projectile to a minimum of one side or yet another or sluggish it or push it alongside. It gets very complicated once you talk approximately that there are distinctive winds, temperatures, pressures, and air densities at distinctive elevations, so a cannon firing at a objective 15 miles away would have countless distinctive situations to account for. an thrilling aside, the army's artillery college trains meteorologists for this very reason.

Answer 3

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