34. in a soccer practice session the football is kept at the centre of the field 40 yards from the 10 ft high goalposts.
A goal is attempted by kicking the football at a speed
of 64 ft/s at an angle of 45° to the horizontal. Will the
ball reach the goal post ?
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Answer
The acceleration due to gravity on earth is g=9.8m/s
2
We know that 40yards=120feet
Horizontal range x=120ft
The initial speed of the ball is u=64ft/s
The angle at which the ball is kicked θ=45
0
know that horizontal range x=ucosθt
t=
ucosθ
x
t=
64 cos45
0
120
t=
64×
2
1
120
=
64
120×1.414
=2.65 sec
y=
2gt
2
sinθ(t)−1
=
2×(32.2)×(2.65)
2
sin(45)×2.65−1
=7.08 ft which is less than the eight of goal post.
in time 2.65 sec the ball travels a horizontal distance of 120 ft and vertical height 7.08 ft which is less than 10 ft.
hence, the ball will reach the post.
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