a bullet is fired from a rifle with a speed V0 at a an angle theta with respect

Question

a bullet is fired from a rifle with a speed V0 at a an angle theta with respect to the horizontal axis from a cliff that is height h above the ground below. calculate the speed of the bullet when it hits the ground. expess your answer in terms of v0,h,g and theta. explain why your result is independent of the value of theta.

__ i think that you calculate the Vx but using Vx=Vo*cos(theta) but im not sure it isnt just Vx=Vox ..?? Im pretty sure you get Vy by using Vy^2=(Voy^2)-2g(y-yo) ...am i close??

Explanation / Answer

There is a contradiction in your above statements.
(a) asks for the speed of the bullet when it strikes the ground in terms of several variables, one of which is theta. However, (b) then states that this speed is independent of theta.
I'm sorry - but you can't have it both ways!

Very briefly, the derivation of the answer goes like this.
The bullet leaves the rifle at an angle theta with repect to the horizontal.
Eventually, the bullet will be travelling downwards at a point that is a horizontal distance from the top of the cliff - from where the bullet was first fired. A basic consideration of the Law of Conservation of Energy tells us that at that point, the bullet has a speed of v0 and its path makes an angle of theta below the horizontal.
Therefore, the component of the velocity of the bullet vertically downwards is v0.sin(theta). { The horizontal component of the velocity is v0.cos(theta) }
Call this initial downward velocity u; call the final velocity - when it hits the ground - v. The bullet is subject to the Earth's gravity (g) and it falls thru a distance h.

So . . .we can now write:
v² = u² + 2gh, where u = v0.sin(theta).
v is the velocity upon impact; the horizontal component is not relevant, since it is a horizontal component of the velocity.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.