NEET Motion in a Plane — Set 18

Question 1

A ball is thrown at $ 22 \, \text{m/s} $ at $ 60^\circ $. What is its vertical velocity at $ t = 1.5 \, \text{s} $? (Take $ g = 10 \, \text{m/s}^2, \sin 60^\circ = 0.866 $)

Accepted Answer

Vertical velocity $ v_y = v_0 \sin \theta_0 - g t $. Given: $ v_0 = 22 \, \text{m/s}, \sin 60^\circ = 0.866, t = 1.5 \, \text{s}, g = 10 \, \text{m/s}^2 $. $ v_y = 22 \times 0.866 - 10 \times 1.5 = 19.052 - 15 = 4.05 \, \text{m/s} $.

Question 2

A projectile is launched at $ 14 \, \text{m/s} $ at $ 53^\circ $. What is its time of flight? (Take $ g = 9.8 \, \text{m/s}^2, \sin 53^\circ = 0.8 $)

Accepted Answer

Time of flight $ T_f = \frac{2 v_0 \sin \theta_0}{g} $. Given: $ v_0 = 14 \, \text{m/s}, \sin 53^\circ = 0.8, g = 9.8 \, \text{m/s}^2 $. $ T_f = \frac{2 \times 14 \times 0.8}{9.8} = \frac{22.4}{9.8} \approx 2.29 \, \text{s} $.

Question 3

A projectile is launched at $ 36 \, \text{m/s} $ at $ 37^\circ $. What is its horizontal range? (Take $ g = 12 \, \text{m/s}^2, \sin 74^\circ = 0.96 $)

Accepted Answer

Range $ R = \frac{v_0^2 \sin 2\theta_0}{g} $, where $ 2\theta_0 = 74^\circ $. Given: $ v_0 = 36 \, \text{m/s}, \sin 74^\circ = 0.96, g = 12 \, \text{m/s}^2 $. $ R = \frac{36^2 \times 0.96}{12} = \frac{1296 \times 0.96}{12} = \frac{1244.16}{12} \approx 103.68 \, \text{m} $.

NEET Physics: Motion in a Plane — Practice Set 18

Q1. A ball is thrown at \( 22 \, \text{m/s} \) at \( 60^\circ \). What is its vertical velocity at \( t = 1.5 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2, \sin 60^\circ = 0.866 \))

Q2. A projectile is launched at \( 14 \, \text{m/s} \) at \( 53^\circ \). What is its time of flight? (Take \( g = 9.8 \, \text{m/s}^2, \sin 53^\circ = 0.8 \))

Q3. A projectile is launched at \( 36 \, \text{m/s} \) at \( 37^\circ \). What is its horizontal range? (Take \( g = 12 \, \text{m/s}^2, \sin 74^\circ = 0.96 \))

Q4. What is the significance of the angle of projection in determining the maximum height of a projectile?

Q5. For an object moving in a plane with constant acceleration, what can be said about its path if the acceleration is perpendicular to the initial velocity?

Q6. A projectile is launched at \( 12 \, \text{m/s} \) at \( 37^\circ \). What is its time of flight? (Take \( g = 10 \, \text{m/s}^2, \sin 37^\circ = 0.6 \))

Q7. A projectile is launched at \( 45 \, \text{m/s} \) at \( 30^\circ \). What is its speed at maximum height? (Take \( g = 10 \, \text{m/s}^2, \cos 30^\circ = 0.866 \))

Q8. In uniform circular motion, which quantity is constant in direction?

Q9. A ball is projected at \( 30 \, \text{m/s} \) at \( 53^\circ \). What is the time to reach maximum height? (Take \( g = 10 \, \text{m/s}^2, \sin 53^\circ = 0.8 \))

Q10. A particle starts from rest with an acceleration of \( (5 \hat{i} - 2 \hat{j}) \, \text{m/s}^2 \). What is its displacement magnitude after \( 3 \, \text{s} \)?