Projectile Motion given only x and y distance

In summary, the question involves finding the appropriate values of velocity (v0) and angle (θ) for Luke Skywalker's X-wing fighter in order to drop a bomb into a ventilation shaft on the Death Star. The bomb's path must reach the front edge of the opening and continue towards a point 10m below the opening. The given constraints are that the time must be greater than 30 seconds, θ must be greater than 70°, and the velocity (v0) must be between 100 and 200 m/s. The attempt at a solution involves setting up equations for velocity in the y direction and position in the x and y directions, and using two points on the path to solve for the two unknowns (
  • #1
tbbtfan14
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Homework Statement


The question reads: Luke Skywalker is dropping a bomb down a ventilation shaft on the Death Star. The circular shaft has a diameter of 1m. When the bomb is released, Luke's X-wing start-fighter is 200m above the shaft's opening and 500m horizontally from the front edge of the opening. His ship is traveling at a velocity v0 at an angle θ
above the horizontal. If he wants the bomb to reach the front edge of the opening so that the bomb is moving toward a point on the other side of the shaft that is 10m below the opening, find the appropriate values of v0 and θ.


Homework Equations


Velocity in the y direction: vy = 10vx
x= x0 + ((v0)(cosθ))t
y = y0 +((v0)(sinθ))t + .5at^2


Constraints:
time > 30sec
θ > 70°
100 < (v0) < 200 m/s


The Attempt at a Solution


So far I am stuck at: 200 = 4.9t^2 +10((v0)(cosθ))t. I am trying to get an equation to solve for t, but I seem to end up with two variables (v0 and θ) in one equation when I try. Please help this is due tomorrow (9-18) at 10 am!
 
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  • #2
Maybe we try reverse position.
The origin of frame of refrence at side of the shaft.

y=uyt -0.5at2
x=uxt => t=x/ux

y=uTanθ- 0.5a(x2/(u2Cos2θ)

2 unknowns and we have 2 points on the path equation.
 
Last edited:

1. How do I calculate the initial velocity of a projectile using only the x and y distances?

The initial velocity of a projectile can be calculated using the formula v = √(x^2 + y^2), where x and y are the horizontal and vertical distances traveled by the projectile, respectively. This formula assumes that the initial angle of launch is 45 degrees.

2. Can I use the same formula to calculate the initial velocity if the launch angle is not 45 degrees?

No, the formula for calculating initial velocity only works for a launch angle of 45 degrees. To calculate the initial velocity for a different angle, you will need to use the formula v = √(x^2 + y^2) * sin(θ), where θ is the launch angle in radians.

3. How do I determine the launch angle of a projectile if I only know the x and y distances?

The launch angle can be calculated using the formula θ = tan^-1(y/x). This formula assumes that the initial velocity is known and the initial angle is 45 degrees.

4. What is the equation for finding the maximum height of a projectile with only the x and y distances?

The maximum height of a projectile can be calculated using the formula h = y + (v^2 * sin^2(θ)) / 2g, where h is the maximum height, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

5. Is there a way to calculate the time of flight for a projectile using only the x and y distances?

Yes, the time of flight for a projectile can be determined using the formula t = x / (v * cos(θ)), where t is the time of flight, x is the horizontal distance, v is the initial velocity, and θ is the launch angle.

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