NEET Motion in a Plane — Set 4

Question 1

A projectile is launched with a speed of $ 16 \, \text{m/s} $ at an angle of $ 30^\circ $ to the horizontal. What is its maximum height? (Take $ g = 10 \, \text{m/s}^2, \sin 30^\circ = 0.5 $)

Accepted Answer

Maximum height $ h_m = \frac{(v_0 \sin \theta_0)^2}{2g} $. Given: $ v_0 = 16 \, \text{m/s}, \sin 30^\circ = 0.5, g = 10 \, \text{m/s}^2 $. $ v_0 \sin \theta_0 = 16 \times 0.5 = 8 \, \text{m/s} $. $ h_m = \frac{8^2}{2 \times 10} = \frac{64}{20} = 3.2 \, \text{m} $.

Question 2

An object in uniform circular motion has a radius of 5 m and completes 10 revolutions in 20 s. What is the magnitude of its centripetal acceleration?

Accepted Answer

Angular speed ω = (2π n) / t, where n = 10, t = 20 s. ω = (2π × 10) / 20 = π rad/s. Centripetal acceleration a_c = ω² R = (π)² × 5 ≈ 9.87 × 5 ≈ 49.35 m/s².

Question 3

A projectile is launched at $ 18 \, \text{m/s} $ at $ 45^\circ $. What is its horizontal velocity component?

Accepted Answer

Horizontal velocity $ v_x = v_0 \cos \theta_0 $. Given: $ v_0 = 18 \, \text{m/s}, \cos 45^\circ = \frac{1}{\sqrt{2}} \approx 0.707 $. $ v_x = 18 \times 0.707 \approx 12.73 \, \text{m/s} $.

NEET Physics: Motion in a Plane — Practice Set 4

Q1. A projectile is launched with a speed of \( 16 \, \text{m/s} \) at an angle of \( 30^\circ \) to the horizontal. What is its maximum height? (Take \( g = 10 \, \text{m/s}^2, \sin 30^\circ = 0.5 \))

Q2. An object in uniform circular motion has a radius of 5 m and completes 10 revolutions in 20 s. What is the magnitude of its centripetal acceleration?

Q3. A projectile is launched at \( 18 \, \text{m/s} \) at \( 45^\circ \). What is its horizontal velocity component?

Q4. A particle starts with velocity \( 4 \hat{j} \, \text{m/s} \) and accelerates at \( (3 \hat{i} - 2 \hat{j}) \, \text{m/s}^2 \). What is its speed after \( 2 \, \text{s} \)?

Q5. An object moves in a circular path of radius \( 4 \, \text{m} \) with a frequency of \( 5 \, \text{Hz} \). What is the magnitude of its centripetal acceleration?

Q6. A particle starts from rest with a constant acceleration of \( (2 \hat{i} + 6 \hat{j}) \, \text{m/s}^2 \). What is its speed after \( 2 \, \text{s} \)?

Q7. A ball is thrown horizontally at \( 15 \, \text{m/s} \) from a height of \( 98 \, \text{m} \). What is its horizontal range? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q8. In motion with constant acceleration in a plane, what is true if the acceleration is zero?

Q9. A boat moves north at 20 km/h while a river current flows east at 15 km/h. What is the magnitude of the resultant velocity?

Q10. A particle’s position is given by \( x = 5t - t^2 \) and \( y = 2t^2 \) (in meters and seconds). What is the magnitude of its acceleration?