Question

A raft is moving in a river with speed of 10 m/s and a cycle is moving 10 m/s x with a speed of 15 m/s in the direction shown. (A the speed of the river as seen by the cyclist is N565 m/s. (B) the velocity of the river as seen by the cyclist is at an angle tan' from x-axis. (C) the speed of the river as seen by the cyclist is 325 m/s. (D) the velocity of the river as seen by the cyclist is at an angle 53° from x-axis.

Answer 1

Answer: (A) ,(B)

Explanation:

This question seems to be of multiple type. (more than one correct)

Full Question is  attached .

1) We have,

Velocity of Raft,

$\vec{V_R}=10i$

Velocity of Cycle,

$\vec{V_C}=-15cos(37^{\circ})i-15sin(37^{\circ})j\\ \\=-12i-9j$

2)Now, We will calculate velocity of raft with respect to cycle,

$\vec{V_{RC}}=\vec{V_{R}}-\vec{V_{C}}\\ \\=10i-(-12i-9j)=22i+9j$

That is,

Speed

$|\vec{V_{RC}}|=\sqrt{(22^2+9^2)}=\sqrt{565}m/s$

Required Angle

$=tan^{-1}(\frac{v_y}{v_x})=tan^{-1}(\frac{9}{22})$

Hence, Options A and B are correct .