Projectile Motion Analyzation Problem

[Not a Wrench]

Homework Statement

A cannonball is fired out of a cannon at 45 m/s at an angle theta in the positive x direction 500 meters away from a car moving in the positive x at a constant 20 m/s. At what distance does the cannonball hit the car?

Homework Equations

I am unsure of how I would solve theta.

The Attempt at a Solution

O= theta
I tried to use the range formula: d=V^2/g * sin(2O)
So I plugged in all the numbers and it's impossible to do that. sin(2O)=2.42 which is impossible. Is it impossible to figure this out if just given the Vo?

 

[SteamKing]

Homework Statement

A cannonball is fired out of a cannon at 45 m/s at an angle theta in the positive x direction 500 meters away from a car moving in the positive x at a constant 20 m/s. At what distance does the cannonball hit the car?

Homework Equations

I am unsure of how I would solve theta.

The Attempt at a Solution

O= theta
I tried to use the range formula: d=V^2/g * sin(2O)
So I plugged in all the numbers and it's impossible to do that. sin(2O)=2.42 which is impossible. Is it impossible to figure this out if just given the Vo?

You should be able to select θ to give the maximum range of the cannonball when it is fired at 45 m/s.

At this maximum range, is the cannonball capable of reaching the car, assuming the car is 500 m from the cannon and the car is stopped?

What will change if the car starts moving just as the cannon is shot?

What can you conclude about the speed of the cannonball as it leaves the cannon?

 

[tommyxu3]

The distance that the ball runs finally, that is, your $d,$ should be equal to the original distance the car from you and the distance it makes during the time, which may be what you miss.
But I'm also not sure how to deal with these 2 variables $\theta$ and $t$ with the only relation...

 

[SteamKing]

The distance that the ball runs finally, that is, your $d,$ should be equal to the original distance the car from you and the distance it makes during the time, which may be what you miss.
But I'm also not sure how to deal with these 2 variables $\theta$ and $t$ with the only relation...

You should not assume automatically that a cannonball fired with an initial velocity of 45 m/s will be able to cover 500 m.

That's why I suggested that the range formula should be used in conjunction with the angle which gives the maximum range to see if the cannonball is in fact capable of reaching 500 m. The answer may surprise you.