Motion in Two Dimensions of darts

In summary, the dart is thrown with an initial velocity that is inclined upwards and the maximum height of the trajectory is at the vertex of a parabola.
  • #1
Keithkent09
33
0

Homework Statement


In the game of darts, the player stands with feet behind a line 2.36 m from a dartboard, with the bull's-eye at eye level. Suppose you lean across the line, release a dart at eye level 2.23 m from the board, and hit the bull's-eye. Find the initial velocity of the dart, if the maximum height of its trajectory is 1.45 cm above eye level

Homework Equations


y=v_0t+.5gt^2
x=v_0t
v_f=v_i+at
v_f^2=v_i^2+2ax

The Attempt at a Solution


I tried to find the angle at which the projectile was thrown by using inverse tangent of .0145/1.115 but that did not give me the correct angle. I tried plugging in these numbers and manipulating the equations but I could not get anything to work out.
 
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  • #2
Here's some hints: the trajectory of the dart is a parabola. The maximum height of the dart is at the vertex of the parabola. Your initial velocity will be inclined upwards from the horizontal and you will need to use two kinematic equations.
 
  • #3
Okay, I tried to use the two kinematics already but had no success. I only have two equations and three variables. I tried to substitute v_icostheta for the v_i in the x direction and v_isintheta for the v_i in the y direction and could not get anything to work. I am sorry I really am trying to learn this.
 
  • #4
Keithkent09 said:
Okay, I tried to use the two kinematics already but had no success. I only have two equations and three variables. I tried to substitute v_icostheta for the v_i in the x direction and v_isintheta for the v_i in the y direction and could not get anything to work. I am sorry I really am trying to learn this.

Well, here are a couple more hints. The t variable is the same in both equations. The time taken to get to the top of the parabolic path is one-half the total time of flight. You should write two equations:

[tex] X = X_0 + V_{0x} t + \frac{1}{2} a_x t^2 [/tex]

and

[tex] Y = Y_0 + V_{0y} t + \frac{1}{2} g t^2 [/tex]

Take the origin at the point of release and [itex] Y_0 = 0 [/itex] as does [itex] X_0 [/itex].

Also [itex] a_x = 0 [/itex].

Now eliminate t, and you should be able to find your answer. If that doesn't do it for you, post a response and I'll look at it again later today.
 
Last edited:

1. How is motion in two dimensions of darts measured?

Motion in two dimensions of darts is typically measured using the distance and direction of the dart's movement. This can be done by measuring the horizontal and vertical components of the dart's displacement, as well as its velocity and acceleration in both directions.

2. What factors affect the motion of a dart in two dimensions?

The motion of a dart in two dimensions can be affected by various factors such as air resistance, gravity, and the force and angle with which the dart is thrown. Other factors like wind speed and direction can also have an impact on the dart's trajectory.

3. How does air resistance affect the motion of a dart in two dimensions?

Air resistance, also known as drag, can slow down the motion of a dart in two dimensions, as it creates a force that acts in the opposite direction of the dart's movement. The amount of air resistance depends on the shape and speed of the dart, as well as the density of the air.

4. Can a dart's motion in two dimensions be predicted accurately?

Yes, the motion of a dart in two dimensions can be predicted accurately using mathematical equations and principles such as projectile motion and Newton's laws of motion. However, factors such as air resistance and external forces can make the prediction less precise.

5. How does the surface on which the dart is thrown affect its motion in two dimensions?

The surface on which the dart is thrown can affect its motion in two dimensions by providing more or less friction, which can impact the dart's speed and direction. A smooth surface will have less friction, allowing the dart to travel further, while a rough surface will have more friction, causing the dart to slow down and potentially change direction.

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