Question

5. A man rides a jet boat with a speed of 40 km/hr in the north-east direction and the shore line make angle of 10° south of east. Find the component of the velocity of the jet boat
i ) along the shoreline,
(ii) perpendicular to the shoreline,​

Answer 1

ANSWER:

The component of the velocity of the jet boat

• (i) along the shoreline = 22.8 kmph

• (ii) perpendicular to the shoreline = 32.8 kmph

GIVEN:

• A man rides a jet boat with a speed of 40 km/hr in the north-east direction.

• The shore line make angle of 10° south of east.

TO FIND:

The component of the velocity of the jet boat

• (i) along the shoreline.

• (ii) perpendicular to the shoreline.

EXPLANATION:

(i)The component of the velocity of the jet boat along the shoreline.

( Refer attachment 1 )

The component of the velocity of the jet boat along the shoreline is $V_b \cos(55^{\circ})$

$V_b$ = velocity of boat = 40 kmph

Cos 55° = 0.57

$V_b \cos(55^{\circ}) = 40 \times 0.57$

$V_b \cos(55^{\circ}) = 22.8\ kmph$

The component of the velocity along the shoreline = 22.8 kmph.

(ii)The component of the velocity of the jet boat perpendicular to the shoreline.

( Refer attachment 2 )

The component of the velocity of the jet boat perpendicular to the shoreline $V_b \sin(55^{\circ})$

$V_b$ = velocity of boat = 40 kmph

Sin 55° = 0.82

$V_b \sin(55^{\circ}) = 40 \times 0.82$

$V_b \sin(55^{\circ}) = 32.8 \ kmph$

(ii)The component of the velocity along the shoreline = 32.8 kmph.