# 2D Kinematics Problem (Projectile Motion)

## 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!

danago
Gold Member
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.

HallsofIvy
Homework Helper

## 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!