Question

In a soccer practice session the football is kept at the center 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 goalpost ?Concept of Physics - 1 , HC VERMA , Chapter "Rest and Motion : Kinematics

Answer 1

Solution:

g=9.8m/s2 =32.2ft /s2
40 yards=120 feet
Horizontal range =x=120 ft 
u=64 ft/s
θ=45°
we know that horizontal range , x=u cosθ t
t=x/ucos θ
t=120/64 cos45 °
t=120 /64 x 1/√2
=120x 1.414/64
=2.65sec
y=sinθ(t)-1/2gt²
=sin(45) x 2.65 -1/2 (32.2)(2.65)²=7.08 ft which is less than the eight of goal post.
In time 2.65 sec the ball travels a horizontal distance 120ft and vertical height 7.08ft which is less than 10ft. 
Hence the ball will reach the goal post.

Answer 2

HEY!!

____________________________

▶Height of the goalpost = 10 ft

✔The football is kept at a distance of 40 yards.

☛40 yards = 120ft

✔Initial speed (u) with which the ball is hit =
64ft/s

✔Acceleration  a = g = 9.8 m/s^2 = 32.2 ft/s^2

✔40 yards is the horizontal range (R).

✔Angle of projection (α) = 45°

✔Horizontal range is given by:- R = ucosα(t)

t=R/ucosα     
t=120/64 cos 45° =2.65 s

✔Vertical distance covered by the football:-

y=usinα(t) - 1gt^2

=64×(1/root2 bar) ×2.65 −1/2 × 32.2×(2.65)^2

▶Height of the goalpost = 6.86 ft

▶▶Yes, the football will reach the goalpost.