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- Thread starter Towk667
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In summary, you are given the distance from the bottom of the cliff, the initial velocity, and the height of the cliff. You use an equation to find the angle at which the object was shot.

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you can then work backwards to find theta.

start with splitting the initial velocity into orthogonal components.

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Towk667 said:

These equations might be a useful resource for you:

https://www.physicsforums.com/showpost.php?p=905663&postcount=2

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Towk667 said:

Typically the trig identity

2*sinθ*cosθ = sin2θ

is of use in resolving Range equations.

Without seeing your work, there's no useful way to help you with what you are doing that I can see.

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or just remember that sin(x)/cos(x) = tan(x)

edit: yeah or the trig identity posted above

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I tried to solve this equation for Θ and get:

(gR)/(V0^{2})=.5sin2Θ+sqrt(sin^{2}Θ+((2gh)/V0))

Am I using the wrong equation or there another trig identity or what?

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{[ucosӨ * sqrt(u^2sin^2Ө + 2gh)] +[2u^2sin2Ө]}/2g = R

I don't know what to do ahead of this, but I'm quite sure this is the correct equation.

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"What is the average velocity of a projectile between the instants it crosses half the maximum height? It is projected with a speed 'u' at an angle Ө with the horizontal"

(a) u sinӨ (b) u cosӨ (c) u tanӨ (d) u

Could I get some help on this one? I don't even know where to start.

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modulus said:

"What is the average velocity of a projectile between the instants it crosses half the maximum height? It is projected with a speed 'u' at an angle Ө with the horizontal"

(a) u sinӨ (b) u cosӨ (c) u tanӨ (d) u

Could I get some help on this one? I don't even know where to start.

I think I can help with this one. Think about the formula to find maximum height and then use that knowledge and a formula for final velocity that doesn't use time to get your answer.

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Towk667 said:I think I can help with this one. Think about the formula to find maximum height and then use that knowledge and a formula for final velocity that doesn't use time to get your answer.

I did what you said and got the following equation for the final velocity:

sqrt{ [ (2g (u sinӨ)^2) + (2g (u cosӨ)^2) - ((u sinӨ)^2)] / 2g }

Now, what do I do? I don't think I can use the final velocity to evaluete the average velocity, right?

Is there any other method in which I can find the total distance and total time?

Projectile motion is the motion of an object through the air under the influence of gravity. It follows a parabolic path due to the acceleration of gravity.

A cannon off a cliff demonstrates projectile motion because the cannonball is launched at an angle from the cliff and falls under the force of gravity, following a parabolic path.

The factors that affect the trajectory of a projectile off a cliff include the initial velocity, angle of launch, and the acceleration of gravity. Air resistance can also have an impact on the trajectory.

The range of a projectile off a cliff can be calculated using the equation: range = (initial velocity squared * sine of twice the launch angle) divided by the acceleration of gravity.

Yes, the height of the cliff can affect the projectile's trajectory. A higher cliff will result in a longer flight time, which can impact the range and landing position of the projectile.

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