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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?

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?

Grade:11

2 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago
Sol. g = 9.8 m/s2, 32.2 ft/s2 ; 40 yd = 120 ft horizontal range x = 120 ft, u = 64 ft/s, θ = 45° We know that horizontal range X = u cos θt ⇒ t = (x )/(u cos⁡θ ) = (120 )/(64 〖 cos 〗⁡〖45°〗 ) = 2.65 sec. y = u sin θ (t) – 1/2 gt2 = 64 1/(√2 (2.65)) – ½ (32.2) (2.65)2 = 7.08 ft which is less than the height of goal post. In time 2.65, the ball travels horizontal distance 120 ft (40 yd) and vertical height 7.08 ft which is less than 10 ft. The ball will reach the goal post.
Karthika
14 Points
4 years ago
H=10ftDist. =40 yard that is 120 ftTheta=45°U^2sin^2(45°)/2(10) = u^2 sin 2 (45°)/1014400/2*10*2=3976/10360=397.6Hence the ball will reach the goal post.

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