How Do You Calculate Projectile Motion for a Cannonball?

[mattwild]

Homework Statement

A cannon has a launch speed of 500m/s and is aimed at a target 2.8km away.
a. Write an equation for the maximum horizontal range of the cannon as a function of the launch angle theta.
b. At what angle must the cannon be launched in order to hit the target?
c. As viewed from above, how quickly does the cannonball's shadow move along the ground?
d. How fast is the cannonball moving when it hits its target?

Homework Equations

D = vit+1/2at^2
velocity formulas

Range of a projectile

The Attempt at a Solution

a. I used the range of a projectile motion and got v^2sin2(theta)/g but I don't know how to make it a function of the launch angle theta. Am I overreading?
b. I am assuming you just plug in the values from the first formula you get.
c. Just find the acceleration?
d. Just find the vf?

 

[mfb]

a. I used the range of a projectile motion and got v^2sin2(theta)/g but I don't know how to make it a function of the launch angle theta. Am I overreading?

d= v^2sin2(theta)/g is a formula for the range as function of the launch angle (and constants). I used d= with d as range to make a formula out of your expression.

b. I am assuming you just plug in the values from the first formula you get.

Right.

c. Just find the acceleration?

Why acceleration?

d. Just find the vf?

There is an easier way, but that works as well.

 

[mattwild]

Because it asks how quickly does the cannonball's shadow move along the ground so I am assuming that means acceleration? Because its velocity is constantly changing so it can't be that

 

[mfb]

Because it asks how quickly does the cannonball's shadow move along the ground so I am assuming that means acceleration?

No, that certainly means velocity. The velocity of the shadow is not changing here if the sun is shining vertically.