Question

To win the game, a place kicker must kick a football from a point 45 m (49.212 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 24 m/s at an angle of 32.6 ◦ from the horizontal. The acceleration of gravity is 9.8 m/s 2 . By how much vertical distance does the ball clear the crossbar? Answer in units of m.

Answer 1

Answer:

1.65m

Step-by-step explanation:

First, we have to know the velocity of the ball in both axis, x-axis and y-axis.

Vy = sen(32.6°)*24m/s =  12.9m/s

Vx = cos(32.6°)*24m/s = 20.2m/s

Now, we are told the distance covered by the ball, which es 45m (x-axis). With that info, we can find the time the ball traveled, by x=v*t

x = distance in x-axis and  Vx = 16.85m/s

Clearing t, we have: t = x / Vx = 45m / 20.2m/s = 2.2s

Finally, using the equation of vertical distance: Dy = 1/2 a*t² + V0y*t

Dy = (1/2*-9.8m/s²*2.2s²) + 12.9m/s*2.2s = -23.7m + 28.4m = 4.7m

The ball cleared the croosbar by 4.7m-3.05= 1.65m