Calculation Question A soccer player kicks the ball towards the goal located 35m

Question

Calculation Question A soccer player kicks the ball towards the goal located 35m away. He is directly in front of the goal and kicks the ball directly towards the goal. The ball leaves his foot 25cm above the ground at an angle of 55 degrees with respect to the horizontal. To be sure the shot passes over the goalkeeper the ball needs to be 2 meters above the ground when it is 3 meters from the goal. a) How fast must the ball launched to make the shot? b) Does the ball reach the ground before or after crossing the goal opening? Calculation Question A sailboat is moving along the surface of the water with a velocity of 3m/s towards the east. A dolphin is swimming along the surface of the water - ahead of the boat - with a velocity of 1m/s with respect to the boat. A seagull is flying towards the sailboat from the northwest direction with a speed of 6m/s with respect to the boat. The seagull does not change elevation. a) What is the velocity of the seagull with respect to the dolphin?

Explanation / Answer

Net elevation=2-0.25=1.75m

Distance at this elevation=35-3=32m

By equation of trajectory,

1.75=32Tan55-9.81*32^2/(2*v^2*Cos^2(55))

Solving for v,

v=18.64m/s

b)Again using equation to trajectory to find height at the distance of goal,

y=35Tan55-9.81*35^2/(2*18.64^2*Cos^2(55))=-2.58m.

The negative value at distance to goal indicates that the ball hits ground before crossing goal opening.

2)Velocity of dolphin wrt water=1+3=4m/s i

Velocity of seagull in x direction=(6*(1/sqrt(2))-3) i- 6*(1/sqrt(2)j=1.243m/s i-4.243 m/s j

Velocity of seagull wrt dolphin=(1.243-4)i-4.243j

magnitude=5.06m/s

Direction=Tan^-1(4.243/2.757)=57 degrees south of west.

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