Finding t for projectile motion without initial velocity

In summary, the problem involves an arrow being shot at an angle of 45 degrees above the horizontal and hitting a tree 220m away at the same height it was shot. The goal is to find the time the arrow spends in the air, using the given value of 9.8m/s^2 for the acceleration due to gravity. Equations related to initial velocities and displacement can be used to solve for Δt. However, the student is struggling to find a suitable equation and is seeking guidance on how to approach the problem.
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vsindorf
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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.
 
Physics news on Phys.org

What is projectile motion and why is it important in science?

Projectile motion is the motion of an object that is launched into the air and then moves under the influence of gravity. It is important in science because it helps us understand the motion of objects in the real world, such as a ball thrown by a pitcher or a cannonball fired from a cannon.

What is the formula for finding t in projectile motion without initial velocity?

The formula for finding t in projectile motion without initial velocity is t = √(2h/g), where t is the time of flight, h is the vertical displacement, and g is the acceleration due to gravity.

Why is it sometimes necessary to find t in projectile motion without initial velocity?

In some situations, the initial velocity of the projectile is unknown or difficult to measure. In these cases, it is necessary to find t in order to calculate other important factors such as the maximum height or range of the projectile.

What are the units for t in projectile motion without initial velocity?

The units for t in projectile motion without initial velocity are usually in seconds (s) since it represents the time of flight.

Are there any limitations to using the formula for finding t in projectile motion without initial velocity?

Yes, the formula assumes that there is no air resistance and the projectile is only influenced by the force of gravity. In real-world scenarios, there may be other factors that affect the motion of the projectile, so the results may not be completely accurate.

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