A BALL OF MASS 0.5 KILOGRAM, INITIALLY AT REST, IS KICKEDDIRECTLY TOWARD A FENCE

Question

A BALL OF MASS 0.5 KILOGRAM, INITIALLY AT REST, IS KICKEDDIRECTLY TOWARD A FENCE FROM A POINT 32 METERS AWAY. THEVELOCITY OF THE BALL AS IT LEAVES THE KICKER'S FOOT IS 20 METERSPER SECOND AT AN AGLE OF 37 DEGREES ABOVE THE HORIZONTAL. THETOP OF THE FENCE IS 2.5 METERS HIGH. THE KICKER'S FOOT IS INCONTACT WITH THE BALL FOR 0.05 SECOND. THE BALL HITS NOTHINGWHILE IN FLIGHT AND AIR RESISTANCE IS NEGLIGIBLE. A) DETERMINE THE MAGNITUDE OF THE AVERAGE NET FORCE EXERTED ONTHE BALL DURING THE KICK. B) DETERMINE THE TIME IT TAKES FOR THE BALL TO REACH THE PLANEOF THE FENCE. C) WILL THE BALL HIT THE FENCE? IF SO, HOW FAR BELOW THE TOPOF THE FENCE WILL IT HIT? IF NOT, HOW FAR ABOVE THE TOP OF THEFENCE WILL IT PASS? A BALL OF MASS 0.5 KILOGRAM, INITIALLY AT REST, IS KICKEDDIRECTLY TOWARD A FENCE FROM A POINT 32 METERS AWAY. THEVELOCITY OF THE BALL AS IT LEAVES THE KICKER'S FOOT IS 20 METERSPER SECOND AT AN AGLE OF 37 DEGREES ABOVE THE HORIZONTAL. THETOP OF THE FENCE IS 2.5 METERS HIGH. THE KICKER'S FOOT IS INCONTACT WITH THE BALL FOR 0.05 SECOND. THE BALL HITS NOTHINGWHILE IN FLIGHT AND AIR RESISTANCE IS NEGLIGIBLE. A) DETERMINE THE MAGNITUDE OF THE AVERAGE NET FORCE EXERTED ONTHE BALL DURING THE KICK. B) DETERMINE THE TIME IT TAKES FOR THE BALL TO REACH THE PLANEOF THE FENCE. C) WILL THE BALL HIT THE FENCE? IF SO, HOW FAR BELOW THE TOPOF THE FENCE WILL IT HIT? IF NOT, HOW FAR ABOVE THE TOP OF THEFENCE WILL IT PASS?

Explanation / Answer

A BALL OF MASS 0.5 KILOGRAM, INITIALLY AT REST, IS KICKEDDIRECTLY TOWARD A FENCE FROM A POINT 32 METERS AWAY. THEVELOCITY OF THE BALL AS IT LEAVES THE KICKER'S FOOT IS 20 METERSPER SECOND AT AN AGLE OF 37 DEGREES ABOVE THE HORIZONTAL. THETOP OF THE FENCE IS 2.5 METERS HIGH. THE KICKER'S FOOT IS INCONTACT WITH THE BALL FOR 0.05 SECOND. THE BALL HITS NOTHINGWHILE IN FLIGHT AND AIR RESISTANCE IS NEGLIGIBLE. A) DETERMINE THE MAGNITUDE OF THE AVERAGE NET FORCE EXERTED ONTHE BALL DURING THE KICK.
force=change in the momentum/time =0.5*20/0.05=200N
B) DETERMINE THE TIME IT TAKES FOR THE BALL TO REACH THE PLANEOF THE FENCE
time =horizontal distance/horizontalvelocity=32/20cos37=2.003sec. C) WILL THE BALL HIT THE FENCE? IF SO, HOW FAR BELOW THE TOPOF THE FENCE WILL IT HIT? IF NOT, HOW FAR ABOVE THE TOP OF THEFENCE WILL IT PASS?
maximum height=usin/g=20sin37/9.8=1.2281m
as the height of the fence is 2.5m
the ball wont cross it .
it hits the fence at a height 2.5-1.228=1.271m below thetop.

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