You kick a ball with a speed of 18 m/s at an angle of 32°. How far away does the ball land?

Question

whpalmer4 · Answer

Do you know how to decompose that into x and y components?

anonymous · Answer

No

whpalmer4 · Answer

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Can you use your knowledge of the basic trig ratios to find $x$ and $y$ from that triangle?

whpalmer4 · Answer

Once you do that, you have two equations to work with.  One describes the height of the ball, and the other describes the horizontal position of the ball.  You solve the first one to find out the value of $t$ when the ball next makes contact with the ground ($h=0$) which gives you the time of flight.  Then you use $d = rt$ to find the distance traveled, where $r$ is the x component you found from the triangle.

whpalmer4 · Answer

The height of the ball will be given by the standard equation
$$h(t) = -\frac{1}{2}gt^2 + v_0 t + h_0$$where $g = 9.8 \text{m/s}^2$, $h_0 = 0$ because the ball starts on the ground, and $v_0$ is the y component you found above.