Finding Range of Object Shot at 40° Angle

[Want to learn]

Homework Statement

An object is shot from the origin with a velocity of 50.0 m/s at an angle of 40.0 degrees above the horizontal. What is the range of the object?

Homework Equations

All the 2D Motion equations - too many to write all out. Ex:

V_x = V_0x + a_xt

The Attempt at a Solution

I don't even think there is enough information given to solve this. I can only solve for
V_x which is 50 * cos 40 = 38.3 from there I don't know where to go. I try to figure out the y components of this motion, but we don't really know anything about y. We can't really find V_y because to find that we need the equation V_y = v_0 sin \theta - gt but we don't know the time.

 

[Kalvarin]

To work out the range we need to work out the flight time. So first find the time it takes the ball to reach it's highest point using the y-component of it's velocity. Then calculate how long it takes to hit the floor. The sum of these two times is the flight time.

 

[Want to learn]

To work out the range we need to work out the flight time. So first find the time it takes the ball to reach it's highest point using the y-component of it's velocity. Then calculate how long it takes to hit the floor. The sum of these two times is the flight time.

ARRRGGGHHHHH - silly me. How could I miss that?

Thank you for pointing me in the right direction, much appreciated m8.

 

[Kalvarin]

ARRRGGGHHHHH - silly me. How could I miss that?

Thank you for pointing me in the right direction, much appreciated m8.

Np :)

 

[RoyalCat]

An simpler, more fruitful approach would be to develop two equations, and then turn them into one.

One would be x(t), the other would be y(t) and combining them will give you y(x)

That function will describe the height of the object above the the origin as a function of its x-axis distance from the origin. Once you have that function, you can just set y=0 to find the x for which this holds true (The range.)

To get you started, I'll just rewrite your equation:

x(t)=v_0\cos{\theta}\cdot t

t=\frac{x}{v_0\cos{\theta}}

From here, you should be all set.