NEET Motion in a Plane — Set 11

Question 1

For an object in uniform circular motion, what is the direction of the velocity vector relative to the acceleration vector?

Accepted Answer

In uniform circular motion, the velocity vector is tangential to the circular path, while the centripetal acceleration is directed towards the center. Thus, the velocity and acceleration vectors are perpendicular to each other at every point.

Question 2

A boat travels west at $ 6 \, \text{m/s} $ while a current flows south at $ 8 \, \text{m/s} $. What is the magnitude of the boat’s velocity relative to the ground?

Accepted Answer

Velocity components: $ v_x = -6 \, \text{m/s}, v_y = -8 \, \text{m/s} $. Magnitude $ v = \sqrt{v_x^2 + v_y^2} = \sqrt{(-6)^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \, \text{m/s} $.

Question 3

In projectile motion, what is the effect of launching at complementary angles (e.g., 30° and 60°) on the range?

Accepted Answer

For complementary angles ($ \theta $ and $ 90^\circ - \theta $), $ \sin 2\theta = \sin (180^\circ - 2\theta) $, so $ R = \frac{v_0^2 \sin 2\theta}{g} $ is the same (e.g., $ \sin 60^\circ = \sin 120^\circ $). Thus, the range remains the same for complementary angles.

NEET Physics: Motion in a Plane — Practice Set 11

Q1. For an object in uniform circular motion, what is the direction of the velocity vector relative to the acceleration vector?

Q2. A boat travels west at \( 6 \, \text{m/s} \) while a current flows south at \( 8 \, \text{m/s} \). What is the magnitude of the boat’s velocity relative to the ground?

Q3. In projectile motion, what is the effect of launching at complementary angles (e.g., 30° and 60°) on the range?

Q4. A projectile is launched with a speed of 50 m/s at 45°. What is its horizontal range? (Take g = 10 m/s²)

Q5. A boy throws a ball with a speed of 20 m/s at an angle of 30° to the horizontal. What is the maximum height reached by the ball? (Take g = 10 m/s²)

Q6. A particle moves in the x-y plane with a constant acceleration of (2 î + 3 ĵ) m/s². If it starts from rest at the origin, what is its speed after 2 s?

Q7. A projectile is launched at \( 30 \, \text{m/s} \) at \( 45^\circ \). What is its time to reach maximum height? (Take \( g = 10 \, \text{m/s}^2, \sin 45^\circ = 0.707 \))

Q8. In uniform circular motion, what is true about the direction of the net force relative to the velocity?

Q9. In projectile motion, what is true about the horizontal component of velocity throughout the trajectory?

Q10. A projectile is launched with a speed of \( 32 \, \text{m/s} \) at \( 60^\circ \) to the horizontal. What is its maximum height? (Take \( g = 10 \, \text{m/s}^2, \sin 60^\circ = 0.866 \))