# Steep and shallow trajectories

1. Oct 11, 2011

### jumbo123

1. The problem statement, all variables and given/known data
A ball is launched at a speed of 10ms-1. It lands 5m away. Find the two possible values of the angle, θ, which the initial trajectory makes with the horizontal.

2. Relevant equations
The equations of motion.

3. The attempt at a solution
I realise that I need to find the angle θ and then use sin(180-θ) to find the other possible angle however I do not know how to get it.

2. Oct 11, 2011

### 1MileCrash

Interesting problem.

What I'd do is set up a system of equations. You know that the time it takes for the ball the fall and the time it takes for the ball to travel 5 m is the same, right? So, build two position equations and solve for t, then set them equal to each other, leaving only one variable, your angle.

Keeping the angle as a variable, theta, can you come up with two functions, one for the y position and one for the x position? What should the values of these functions as a whole be for each one?

What part of the 10 m/s is horizontal? Which part of the 10 m/s is vertical?

3. Oct 11, 2011

### jumbo123

What I don't understand is how to split to 10m/s into hortizontal and vertical componants in order to get the time.

4. Oct 11, 2011

### 1MileCrash

10 meters per second is the magnitude of the vector. Its the same concept as the hypotenuse of a triangle.

5. Oct 11, 2011

### Staff: Mentor

See the "Range and Height" figure at this introductory page:

http://en.wikipedia.org/wiki/Trajectory

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