15.7k views
5 votes
011 10.0 points

To win the game, a place kicker must kick a
football from a point 52 m (56.8672 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 25 m/s at
an angle of 35.9° from the horizontal.
The acceleration of gravity is 9.8 m/s.
By how much vertical distance does the ball
clear the crossbar?
Answer in units of m.

I’m really confused please help me understand these steps for my quiz!

User Ixaxaar
by
5.2k points

1 Answer

3 votes

Answer:

2.47 m

Step-by-step explanation:

Let's calculate first the time it takes for the ball to cover the horizontal distance that separates the starting point from the crossbar of d = 52 m.

The horizontal velocity of the ball is constant:


v_x = v cos \theta = (25)(cos 35.9^(\circ))=20.3 m/s

and the time taken to cover the horizontal distance d is


t=(d)/(v_x)=(52)/(20.3)=2.56 s

So this is the time the ball takes to reach the horizontal position of the crossbar.

The vertical position of the ball at time t is given by


y=u_y t - (1)/(2)gt^2

where


u_y = v sin \theta =(25)(sin 35.9^(\circ))=14.7 m/s is the initial vertical velocity

g = 9.8 m/s^2 is the acceleration of gravity

And substituting t = 2.56 s, we find the vertical position of the ball when it is above the crossbar:


y=(14.7)(2.56) - (1)/(2)(9.8)(2.56)^2=5.52 m

The height of the crossbar is h = 3.05 m, so the ball passes


h' = 5.52- 3.05 = 2.47 m

above the crossbar.

User DNRN
by
5.3k points