Question

Assume that the point of projection and the edge of boat are in same horizontal level.

Solve this !!!

Regards,

TheBlaze

Answer 1

This question is based on projectile motion .

here man 5.5 m away from the center of boat .

so, maximum distance between man and boat ( max range ) = 5.5 + 0.5 = 6 m

and minimum distance between man and boat = 5.5 - 0.5 = 5 m

we know,
Range is distance covered in horizontal direction by projected particle .

e.g R = u²sin2∅/g { from oblique projectile formula }

here you see Range depends upon sin2∅

it means if range maximum then sin2∅ will be maximum . and vice -versa

so,
for maximum angle ,

R = u²sin2∅/g

6 = (10)²sin2∅/10 = 10sin2∅

sin2∅ = 3/5

2tan∅/( 1+tan²∅) = 3/5

10tan∅ = 3 + 3tan²∅

3tan²∅ -10tan∅ +3 = 0
tan∅ = { 10±8)/6 = 3, 1/3

∅ = tan^-1( 3) or tan^-1( 1/3)

again,
for minimum angle ,
5 = (10)²sin2∅/10 = 10sin2∅
sin2∅ = 1/2 = sin30°

∅ = 15°

hence, maximum angle = tan^-1(3)
and minimum angle = 15°

Answer 2

GIVEN:
Length of boat = 1m
Man is sitting 5.5m away from Centre of boat.
Speed = u= 10m/ s
Gravity = g =approx= 10m/s^2
For the apple to fall in boat, the range of projectile should be minimum 5meter and maximum of 6 meters.
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FORMULA TO BE USED:
RANGE = x= u^2 Sin2θ/g
Sin2θ =gx/u^2.
For x=5m:
Sin2θ =10x5/10*10=1/2
Sin2θ =1/2
2θ =30 degrees or 150 degrees
θ =15 degrees or 75 degrees.
For x= 6m:
Sin2θ =10*6/10*10=3/5
Sin2θ =36 degrees or 144 degrees.
θ =18 degrees or 72 degrees.
Therefore, for a perfect shot, minimum angle of projection is 15 degrees and maximum angle of projection should be 75 degrees.
Infact, shots can be made perfect if the minimum angle of projection lies in between 15 degrees to 18 degrees and maximum 72 degrees to 75 degrees.