Question #81756
To win the game, a place kicker must kick a
football from a point 19 m (20.7784 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 15 m/s at
an angle of 51.7
◦
from the horizontal.
The acceleration of gravity is 9.8 m/s
2
.
By how much vertical distance does the ball
clear the crossbar?
football from a point 19 m (20.7784 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 15 m/s at
an angle of 51.7
◦
from the horizontal.
The acceleration of gravity is 9.8 m/s
2
.
By how much vertical distance does the ball
clear the crossbar?
Expert's answer
The trajectory of the ball is given by
y(x)=tan〖(θ)∙x-g/(2v_0^2 cos^2(θ) )〗∙x^2
So
y(19)=tan〖(51.7°)∙19-9.8/(〖2×15〗^2 cos^2(51.7°) )〗∙〖19〗^2
=3.59 m
The vertical distance H that a ball clears the crossbar
H=y(19)-h=3.59-3.05=0.54 m
y(x)=tan〖(θ)∙x-g/(2v_0^2 cos^2(θ) )〗∙x^2
So
y(19)=tan〖(51.7°)∙19-9.8/(〖2×15〗^2 cos^2(51.7°) )〗∙〖19〗^2
=3.59 m
The vertical distance H that a ball clears the crossbar
H=y(19)-h=3.59-3.05=0.54 m
