Question

To win the game, a place kicker must kick a football from a point 56 m (61.2416 yd) from the goal, and the ball must clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 27 m/s at an angle of 31.2◦ from the horizontal. The acceleration of gravity is 9.8 m/s². By how much vertical distance does the ball clear the crossbar? Answer in units of m.'

Answer 1

To calculate how much vertical distance the ball clears the crossbar, we use projectile motion equations to find the maximum height the ball reaches and subtract the height of the crossbar from it.

Step-by-step explanation:

To calculate the vertical distance the ball clears the crossbar, we first need to find the maximum height the ball reaches. We can use the projectile motion equations to calculate this.

First, we find the time of flight using the horizontal component of the initial velocity: t = (2 * v * sin(theta)) / g. Plugging in the values, we get t = (2 * 27 * sin(31.2)) / 9.8 = 1.71 s.

Next, we can find the maximum height using the vertical component of the initial velocity: h = (v^2 * sin^2(theta)) / (2 * g). Plugging in the values, we get h = (27^2 * sin^2(31.2)) / (2 * 9.8) = 11.50 m.

Finally, we can subtract the height of the crossbar from the maximum height to find the vertical distance the ball clears the crossbar: clearance = h - crossbar height = 11.50 - 3.05 = 8.45 m.