NEET Motion in a Plane — Set 15

Question 1

A particle has an initial velocity of 3 î m/s and a constant acceleration of 2 ĵ m/s². What is the magnitude of its displacement after 3 s?

Accepted Answer

Displacement r = v₀ t + (1/2) a t². x = v₀x t = 3 × 3 = 9 m. y = (1/2) a_y t² = (1/2) × 2 × 3² = 9 m. Magnitude |r| = √(x² + y²) = √(9² + 9²) = √162 ≈ 12.73 m.

Question 2

A projectile is launched with a speed of 40 m/s at an angle of 30°. What is its velocity at the highest point? (Take g = 10 m/s²)

Accepted Answer

At the highest point, v_y = 0, v_x = v₀ cos θ₀. Given: v₀ = 40 m/s, cos 30° = √3/2. v_x = 40 × (√3/2) = 20 √3 ≈ 34.64 m/s.

Question 3

A projectile is launched at $ 26 \, \text{m/s} $ at $ 53^\circ $. What is its horizontal velocity component? (Take $ \cos 53^\circ = 0.6 $)

Accepted Answer

Horizontal velocity $ v_x = v_0 \cos \theta_0 $. Given: $ v_0 = 26 \, \text{m/s}, \cos 53^\circ = 0.6 $. $ v_x = 26 \times 0.6 = 15.6 \, \text{m/s} $.

NEET Physics: Motion in a Plane — Practice Set 15

Q1. A particle has an initial velocity of 3 î m/s and a constant acceleration of 2 ĵ m/s². What is the magnitude of its displacement after 3 s?

Q2. A projectile is launched with a speed of 40 m/s at an angle of 30°. What is its velocity at the highest point? (Take g = 10 m/s²)

Q3. A projectile is launched at \( 26 \, \text{m/s} \) at \( 53^\circ \). What is its horizontal velocity component? (Take \( \cos 53^\circ = 0.6 \))

Q4. A ball is thrown horizontally at \( 12 \, \text{m/s} \) from a height of \( 19.6 \, \text{m} \). What is its speed on hitting the ground? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q5. A particle moves in a circular path with a period of \( 4 \, \text{s} \) and radius \( 6 \, \text{m} \). What is its linear speed?

Q6. A projectile is launched at \( 34 \, \text{m/s} \) at \( 60^\circ \). What is its horizontal range? (Take \( g = 9.8 \, \text{m/s}^2, \sin 120^\circ = 0.866 \))

Q7. In motion with constant acceleration in a plane, what is true about the acceleration vector?

Q8. In uniform circular motion, what is the relationship between the velocity vector and the path of the object?

Q9. A particle in circular motion has a centripetal acceleration of \( 25 \, \text{m/s}^2 \) and a speed of \( 10 \, \text{m/s} \). What is the radius of the path?

Q10. A projectile is launched at \( 25 \, \text{m/s} \) at \( 37^\circ \). What is its vertical velocity at \( t = 1 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2, \sin 37^\circ = 0.6 \))