The crossbar challenge is a football contest in which competitors try and hit the crossbar of a goal by kicking a football from the penalty spot - Scottish Highers Physics - Question 1 - 2022

For the vertical component of the initial velocity, we use:

$u_y = u imes ext{sin}( heta)$

Substituting the values:

To find the time, we can use:

$d = u_x imes t$ Where:

• $d = 11$ m (horizontal distance to the crossbar)
• $u_x = 15.5$ m s⁻¹

Rearranging to solve for $t$ gives:

$t = \frac{d}{u_x} = \frac{11}{15.5} \approx 0.71 ext{ s}$

Using the formula for vertical motion:

$s = u_y imes t + \frac{1}{2} a t^2$

In this case, since the vertical motion is upwards against gravity:

• $s = h$ (height above ground)
• $u_y = 6.91$ m s⁻¹
• $a = -9.8$ m s² (acceleration due to gravity)
• $t = 0.71$ s

Substituting the values:

$h = 6.91 imes 0.71 + \frac{1}{2} \times (-9.8) \times (0.71)^2 \approx 2.4 ext{ m}$

If the competitor kicks the football with an initial speed less than 17.0 m s⁻¹ at the same angle, the vertical component of the initial velocity would also decrease. Since the maximum height is dependent on the initial vertical velocity, a smaller initial speed means the height reached will be less than the height of the crossbar (2.4 m).

Thus, the football would pass under the crossbar.