Finding t for projectile motion without initial velocity

AI Thread Summary
To find the time t for the projectile motion of an arrow shot at a 45-degree angle, the horizontal distance D of 220m and the gravitational acceleration g of 9.8m/s² are essential. The horizontal motion can be described using the equation Xf = Xi + (Vx)i*Δt, where (Vx)i is the horizontal component of the initial velocity. Since the arrow lands at the same height it was shot, the vertical motion can be analyzed with Yf = Yi + (Vy)i*Δt - 1/2g(Δt)^2, which simplifies the problem. By recognizing that the horizontal and vertical motions are independent, one can derive the necessary equations to isolate and solve for time t. Understanding these relationships is crucial for determining the time the arrow spends in the air.
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Homework Statement


An arrow is shot at an angle of θ=45* above the horizontal. The arrow hits a tree a horizontal distance D=220m away, at the same height above the ground as it was shot.
Use g=9.8m/s^2 for the magnitude of the acceleration due to gravity.

Find t, the time that the arrow spends in the air (in seconds).

Homework Equations


1) (Vy)i = Vi*sinθ
2) (Vx)i = Vi*cosθ
3) Xf = Xi + (Vx)i*Δt
4) Yf = Yi + (Vy)i*Δt - 1/2g(Δt)^2

The Attempt at a Solution


I have tried going about reconfiguring equations in several different ways to come up with an equation that will give me t, but I'm not doing so well. I don't understand how I can come up with this answer without any information about time, acceleration, or velocity.

any help you can give me to steer me in the right direction for finding components of initial velocity or Δt would be extremely helpful.
 
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