To win the game, a place kicker must kick a
football from a point 51 m (55.7736 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 35.4
◦
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
find the horizontal and vertical components of the launch speed
use the horizontal component to find the flight time (t) to the crossbar
... time = distance / velocity
use the vertical component to find the height of the ball
... h = 1/2 g t^2 + v t ... v is the vertical component of launch velocity
... the 1st term is negative (g is downward acceleration)