a king mackerel jumps out a 3.50m tall fisherman\'s hands with a velocity of 3.0

Question

a king mackerel jumps out a 3.50m tall fisherman's hands with a velocity of 3.00m/s at an angle of 38 degrees in hopes of making an escape back into the water. The fisherman stands 2.9m from the edge of his boat. Does the king mackerel make the escape or will it be served for dinner? a king mackerel jumps out a 3.50m tall fisherman's hands with a velocity of 3.00m/s at an angle of 38 degrees in hopes of making an escape back into the water. The fisherman stands 2.9m from the edge of his boat. Does the king mackerel make the escape or will it be served for dinner? a king mackerel jumps out a 3.50m tall fisherman's hands with a velocity of 3.00m/s at an angle of 38 degrees in hopes of making an escape back into the water. The fisherman stands 2.9m from the edge of his boat. Does the king mackerel make the escape or will it be served for dinner?

Explanation / Answer

let time taken to reach maximum height is t seconds.

at maximum height, vertical speed=0

initial vertical speed=3*sin(38)=1.847 m/s

vertical acceelration=-9.8 m/s^2

==> 0=1.847-9.8*t

==> t=0.1884 seconds

height covered in that time=1.847*t-0.5*9.8*t^2=0.174 m

hence height from ground=3.5+0.174=3.674 m

time taken to travel from maximum height to ground , let be t1.

==> 0*t1+0.5*9.8*t1^2=3.674

==> t1=0.866 seconds

hence net time taken in travelling from the hand of the fisherman to ground level=t+t1=0.1884+0.866=1.0544 seconds

horizontal speed of the fish=3*cos(38)=2.364 m/s

horizontal distance covered in that time=1.0544*3*cos(38)=2.4926 m

as the fisherman is 2.9 m from the shore, the fish wont make it to the water.

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