NEET Motion in a Plane — Set 1

Question 1

A plane flies east at $ 40 \, \text{m/s} $ while a wind blows north at $ 30 \, \text{m/s} $. What is the magnitude of the plane’s velocity relative to the ground?

Accepted Answer

Velocity components: $ v_x = 40 \, \text{m/s}, v_y = 30 \, \text{m/s} $. Magnitude $ v = \sqrt{v_x^2 + v_y^2} = \sqrt{40^2 + 30^2} = \sqrt{1600 + 900} = \sqrt{2500} = 50 \, \text{m/s} $.

Question 2

A stone is projected horizontally with a speed of 10 m/s from a height of 20 m. How long does it take to reach the ground? (Take g = 10 m/s²)

Accepted Answer

For vertical motion: y = v₀y t + (1/2) a_y t², where v₀y = 0, a_y = -g. Given: y = -20 m, g = 10 m/s². -20 = 0 - (1/2) × 10 × t² ⇒ -20 = -5 t² ⇒ t² = 4 ⇒ t = 2 s.

Question 3

A stone tied to a string moves in a circle of radius $ 1.5 \, \text{m} $ with a frequency of $ 2 \, \text{Hz} $. What is its centripetal acceleration?

Accepted Answer

Angular speed $ \omega = 2\pi f = 2\pi \times 2 = 4\pi \, \text{rad/s} $. Centripetal acceleration $ a_c = \omega^2 R = (4\pi)^2 \times 1.5 = 16\pi^2 \times 1.5 \approx 236.87 \, \text{m/s}^2 $.

NEET Physics: Motion in a Plane — Practice Set 1

Q1. A plane flies east at \( 40 \, \text{m/s} \) while a wind blows north at \( 30 \, \text{m/s} \). What is the magnitude of the plane’s velocity relative to the ground?

Q2. A stone is projected horizontally with a speed of 10 m/s from a height of 20 m. How long does it take to reach the ground? (Take g = 10 m/s²)

Q3. A stone tied to a string moves in a circle of radius \( 1.5 \, \text{m} \) with a frequency of \( 2 \, \text{Hz} \). What is its centripetal acceleration?

Q4. In uniform circular motion, what is the relationship between centripetal acceleration (\( a_c \)) and angular speed (\( \omega \))?

Q5. A projectile is launched with a speed of \( 10 \, \text{m/s} \) at an angle of \( 45^\circ \) to the horizontal. What is its maximum height? (Take \( g = 10 \, \text{m/s}^2, \sin 45^\circ = 0.707 \))

Q6. A projectile is launched at \( 25 \, \text{m/s} \) at \( 60^\circ \). What is its range? (Take \( g = 10 \, \text{m/s}^2, \sin 120^\circ = 0.866 \))

Q7. A particle starts from rest with a constant acceleration of \( (6 \hat{i} - 4 \hat{j}) \, \text{m/s}^2 \). What is its speed after \( 2 \, \text{s} \)?

Q8. A ball is thrown at 30 m/s at 60° to the horizontal. What is the time of flight? (Take g = 10 m/s²)

Q9. A ball is thrown at \( 35 \, \text{m/s} \) at \( 37^\circ \). What is its time of flight? (Take \( g = 10 \, \text{m/s}^2, \sin 37^\circ = 0.6 \))

Q10. What is the relationship between angular speed (\( \omega \)) and linear speed (\( v \)) in uniform circular motion?

Q11. A particle starts with velocity \( 8 \hat{i} \, \text{m/s} \) and accelerates at \( (2 \hat{j}) \, \text{m/s}^2 \). What is its speed after \( 4 \, \text{s} \)?

Q12. A particle in circular motion has a centripetal acceleration of \( 81 \, \text{m/s}^2 \) and radius \( 9 \, \text{m} \). What is its speed?

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

Q14. A particle’s position is given by \( x = 3t^2 - 4t \) and \( y = 5t \) (in meters and seconds). What is its speed at \( t = 1 \, \text{s} \)?

Q15. In projectile motion, what happens to the kinetic energy at the maximum height compared to the launch point?