NEET Motion in a Plane — Set 3

Question 1

A stone is thrown horizontally at 12 m/s from a 80 m high cliff. How far from the base does it land? (Take g = 10 m/s²)

Accepted Answer

Time to fall: y = (1/2) g t², -80 = (1/2) × 10 × t² ⇒ t² = 16 ⇒ t = 4 s. Horizontal distance x = v_x t = 12 × 4 = 48 m.

Question 2

A projectile is launched at $ 20 \, \text{m/s} $ at $ 53^\circ $. What is its range? (Take $ g = 10 \, \text{m/s}^2, \sin 106^\circ = 0.96 $)

Accepted Answer

Range $ R = \frac{v_0^2 \sin 2\theta_0}{g} $, where $ 2\theta_0 = 106^\circ $. Given: $ v_0 = 20 \, \text{m/s}, \sin 106^\circ = 0.96, g = 10 \, \text{m/s}^2 $. $ R = \frac{20^2 \times 0.96}{10} = \frac{400 \times 0.96}{10} = \frac{384}{10} = 38.4 \, \text{m} $.

Question 3

A particle completes 8 revolutions in $ 4 \, \text{s} $ in a circular path of radius $ 2 \, \text{m} $. What is its linear speed?

Accepted Answer

Frequency $ f = \frac{n}{t} = \frac{8}{4} = 2 \, \text{Hz} $. Angular speed $ \omega = 2\pi f = 2\pi \times 2 = 4\pi \, \text{rad/s} $. Linear speed $ v = \omega R = 4\pi \times 2 = 8\pi \approx 25.13 \, \text{m/s} $.

NEET Physics: Motion in a Plane — Practice Set 3

Q1. A stone is thrown horizontally at 12 m/s from a 80 m high cliff. How far from the base does it land? (Take g = 10 m/s²)

Q2. A projectile is launched at \( 20 \, \text{m/s} \) at \( 53^\circ \). What is its range? (Take \( g = 10 \, \text{m/s}^2, \sin 106^\circ = 0.96 \))

Q3. A particle completes 8 revolutions in \( 4 \, \text{s} \) in a circular path of radius \( 2 \, \text{m} \). What is its linear speed?

Q4. A projectile is launched at \( 20 \, \text{m/s} \) at \( 37^\circ \). What is its horizontal velocity component? (Take \( \cos 37^\circ = 0.8 \))

Q5. In uniform circular motion, what is the role of the centripetal acceleration?

Q6. A particle moves with a constant acceleration of \( (5 \hat{i} + 2 \hat{j}) \, \text{m/s}^2 \) from rest. What is its speed after \( 3 \, \text{s} \)?

Q7. In projectile motion, what is the direction of the velocity vector at the highest point of its trajectory?

Q8. A particle moves in a circle of radius \( 4 \, \text{m} \) with an angular speed of \( 3 \, \text{rad/s} \). What is its centripetal acceleration?

Q9. A ball is thrown horizontally from a tower with a speed of \( 8 \, \text{m/s} \). It lands \( 24 \, \text{m} \) from the base. What is the height of the tower? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. In projectile motion, what is true about the velocity vector just before landing compared to just after launch, assuming level ground?

Q11. A particle starts from rest with a constant acceleration of \( (-2 \hat{i} + 5 \hat{j}) \, \text{m/s}^2 \). What is the magnitude of its velocity after \( 3 \, \text{s} \)?

Q12. A ball is thrown at \( 30 \, \text{m/s} \) at \( 53^\circ \). What is its vertical velocity at \( t = 2 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2, \sin 53^\circ = 0.8 \))

Q13. A particle starts with velocity \( 5 \hat{i} \, \text{m/s} \) and accelerates at \( (4 \hat{j}) \, \text{m/s}^2 \). What is its speed after \( 3 \, \text{s} \)?

Q14. A ball is thrown horizontally at \( 8 \, \text{m/s} \) from a height of \( 12.5 \, \text{m} \). What is its speed on hitting the ground? (Take \( g = 10 \, \text{m/s}^2 \))