Launching a projectile to hit a target moving away from the launch point

In summary, the conversation is about finding the x and y location of a projectile as a function of time using the equations x(t)=ut.cosϴ and y(t)=ut.sinϴ-1/2gt^2. The speaker is unsure how to find an equation for the position of P using these equations and asks for help. Another person suggests using trigonometry to find the height and horizontal distance from (x,y) to P.
  • #1
johnsmith122
2
0
Homework Statement
A ball is launched at A with a speed u at an angle ϴ (from the horizontal). Show that if a point P moves so as to keep d/dt(tanα)=constant, then P will "catch" the ball at point B.
Relevant Equations
tanϴ =tanα+tanβ
DSC_1158.JPG
 
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  • #2
Your attempt appears to be a random sequence of equations, not directed towards solving the problem.
First, find the x and y location of the projectile as a function of time. Don't substitute a value for g, just leave it as g.
Using those equations, find an equation for the position of P as a function of time.
 
  • #3
Thanks for the help. I found the x and y location of the projectile to be x(t)=ut.cosϴ and y(t)=ut.sinϴ-1/2gt^2 but I'm unsure as to how to find an equation for P using this.
 
  • #4
johnsmith122 said:
Thanks for the help. I found the x and y location of the projectile to be x(t)=ut.cosϴ and y(t)=ut.sinϴ-1/2gt^2 but I'm unsure as to how to find an equation for P using this.
Just a bit of trig. What is the height of (x,y) above P? So what is the horizontal distance from (x,y) to P?
 

1. How do you calculate the velocity needed to hit a moving target?

In order to calculate the velocity needed to hit a moving target, you will need to know the distance between the launch point and the target, the speed of the target, and the angle at which the projectile is launched. Using these variables, you can use the equation v = d/t to determine the velocity needed to reach the target.

2. Is it possible to hit a target moving away from the launch point?

Yes, it is possible to hit a target moving away from the launch point. However, the velocity and angle of the projectile must be carefully calculated in order to account for the target's movement.

3. What factors affect the accuracy of hitting a moving target?

There are several factors that can affect the accuracy of hitting a moving target, including the speed and direction of the target, the velocity and angle of the projectile, and external factors such as wind and air resistance. It is important to carefully consider and account for these factors in order to increase the chances of hitting the target.

4. How does the launch angle affect hitting a moving target?

The launch angle plays a crucial role in hitting a moving target. If the angle is too high, the projectile may travel too far and miss the target. If the angle is too low, the projectile may not have enough velocity to reach the target. It is important to calculate the optimal launch angle based on the target's speed and direction.

5. What type of projectile is best for hitting a moving target?

The type of projectile that is best for hitting a moving target depends on various factors such as the distance to the target, the speed of the target, and the desired accuracy. Generally, a projectile with a high velocity and aerodynamic design is most suitable for hitting a moving target. However, it is important to carefully consider all factors before selecting a projectile.

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