Projectile motion equation?

Question

A place kicker must kick the football from a point 32.9 m from the goal and clear a bar 3.00 m above the ground. The ball leaves the ground with a speed of 20.0 m/s at an angle of 53.0 degrees above the horizontal. 

By how much does the ball clear (positive value) or fall short (negative value) of the cross bar? (This is vertical distance above or below the cross bar.)

When it gets to the cross bar, what is the vertical component of the ball's velocity? (Is it rising or falling?)

Anonymous · Accepted Answer

Then, we have...

s_y = 20sin(53°)t - 4.9t²
s_x = 20cos(53°)t

32.9 = 20cos(53°)t
t = 32.9/(20cos(53°))
≈ 2.73 s

So at t ≈ 2.73, we have...

s_y(2.73) = 20sin(53°)(2.73) - 4.9(2.73)²
≈ 7.09

So the vertical component of the position is 7.09 m.  We can say that the projectile passes over the bar.

You should find the vertical component at t = 2.73 seconds by yourself.  The above computation is just for you to show how things work out.  Remember that in order to find the velocity, use this formula:

v_f = v_0 + at

Good luck!

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Projectile motion equation?

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