2D Kinematics Problem (Projectile Motion)

In summary: Call the angle of projection theta, \theta. In terms of theta, write an equation relating the horizontal distance traveled with the time of flight. You will have two unknowns, theta and the time of flight. Again in terms of theta, write an equation for vertical displacement from the start of the motion to the end (net vertical displacement should be zero since the ground is level). Again, you will have two unknown variables, the angle of projection and the time of flight.
  • #1
Dcarroll
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0

Homework Statement


Hi, I'm in a calculus base physics course in college so i thought this forum would be appropriate to post this question. The question is as follows:

"A cannonball leaves the end of the cannon with an initial velocity of 67 m/s. Assuming a level terrain, at what angle(s) to the horizontal must the cannonball be fired to hit a target 402.3 meters away?"


Homework Equations


X=Xo+Vo(t)+(1/2)(a)(t)^2
V=Vo+a(t)
V^2=Vo^2+(2)(a)(X2-X1)


The Attempt at a Solution


Basically i have been struggling with this problem for awhile now and I'm stuck. I wrote out my horizontal and vertical information in an attempt to maybe find the time it takes for the object to reach its target. It turns out there is not enough information to solve for any of the un-known variables in the equations I listed above. I also cannot use SOH-CAH-TOA to solve for the vertical and horizontal velocities because they don't give enough information.

If anyone can help me through the steps on how to solve this it would be great!
 
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  • #2
Call the angle of projection theta, [tex]\theta[/tex].

In terms of theta, write an equation relating the horizontal distance traveled with the time of flight. You will have two unknowns, theta and the time of flight.

Again in terms of theta, write an equation for vertical displacement from the start of the motion to the end (net vertical displacement should be zero since the ground is level). Again, you will have two unknown variables, the angle of projection and the time of flight.
 
  • #3
Dcarroll said:

Homework Statement


Hi, I'm in a calculus base physics course in college so i thought this forum would be appropriate to post this question. The question is as follows:

"A cannonball leaves the end of the cannon with an initial velocity of 67 m/s. Assuming a level terrain, at what angle(s) to the horizontal must the cannonball be fired to hit a target 402.3 meters away?"


Homework Equations


X=Xo+Vo(t)+(1/2)(a)(t)^2
V=Vo+a(t)
V^2=Vo^2+(2)(a)(X2-X1)
X is important, of course, but the last two equations are not relevant. What is relevant, that you have NOT given is the y component. What are the equations for vertical motion?

Also, you need the fact that the x component of initial velocity is V0 cos(theta) and the y component is V0 sin(theta).


The Attempt at a Solution


Basically i have been struggling with this problem for awhile now and I'm stuck. I wrote out my horizontal and vertical information in an attempt to maybe find the time it takes for the object to reach its target. It turns out there is not enough information to solve for any of the un-known variables in the equations I listed above. I also cannot use SOH-CAH-TOA to solve for the vertical and horizontal velocities because they don't give enough information.

If anyone can help me through the steps on how to solve this it would be great!
 

FAQ: 2D Kinematics Problem (Projectile Motion)

1. What is projectile motion?

Projectile motion is the motion of an object in a two-dimensional space under the influence of gravity. It is a combination of horizontal and vertical motion.

2. What is the equation for projectile motion?

The equation for projectile motion is: y = y0 + (v0sinθ)t - 1/2gt2 for the vertical motion and x = x0 + (v0cosθ)t for the horizontal motion, where y and x are the vertical and horizontal positions, y0 and x0 are the initial positions, v0 is the initial velocity, θ is the angle of projection, t is the time, and g is the acceleration due to gravity.

3. What are the key concepts in solving 2D kinematics problems?

The key concepts in solving 2D kinematics problems are: understanding the motion in two dimensions, breaking the motion into horizontal and vertical components, using the equations of motion, and understanding the effects of gravity on the motion.

4. How do you calculate the range of a projectile?

The range of a projectile can be calculated using the equation: R = (v02sin2θ)/g, where R is the range, v0 is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity.

5. How do you determine the maximum height of a projectile?

The maximum height of a projectile can be determined by using the equation: H = (v02sin2θ)/2g, where H is the maximum height, v0 is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity.

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