NEET Motion in a Plane — Set 10

Question 1

A projectile is launched at $ 26 \, \text{m/s} $ at $ 45^\circ $. What is its time to reach maximum height? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Time to maximum height $ t_m = \frac{v_0 \sin \theta_0}{g} $. Given: $ v_0 = 26 \, \text{m/s}, \sin 45^\circ = \frac{1}{\sqrt{2}} \approx 0.707, g = 10 \, \text{m/s}^2 $. $ t_m = \frac{26 \times 0.707}{10} \approx \frac{18.382}{10} \approx 1.84 \, \text{s} $.

Question 2

A particle in circular motion has a centripetal acceleration of $ 100 \, \text{m/s}^2 $ and speed of $ 20 \, \text{m/s} $. What is its radius?

Accepted Answer

Centripetal acceleration $ a_c = \frac{v^2}{R} $. Given: $ a_c = 100 \, \text{m/s}^2, v = 20 \, \text{m/s} $. $ 100 = \frac{20^2}{R} \Rightarrow 100 = \frac{400}{R} \Rightarrow R = \frac{400}{100} = 4 \, \text{m} $.

Question 3

A particle starts from rest with a constant acceleration of (4 î + 2 ĵ) m/s². What is its speed after 5 s?

Accepted Answer

Velocity v = v₀ + at, where v₀ = 0. Given: a = 4 î + 2 ĵ, t = 5 s. v = (4 î + 2 ĵ) × 5 = 20 î + 10 ĵ m/s. Speed v = √(v_x² + v_y²) = √(20² + 10²) = √(400 + 100) = √500 ≈ 22.36 m/s.

NEET Physics: Motion in a Plane — Practice Set 10

Q1. A projectile is launched at \( 26 \, \text{m/s} \) at \( 45^\circ \). What is its time to reach maximum height? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A particle in circular motion has a centripetal acceleration of \( 100 \, \text{m/s}^2 \) and speed of \( 20 \, \text{m/s} \). What is its radius?

Q3. A particle starts from rest with a constant acceleration of (4 î + 2 ĵ) m/s². What is its speed after 5 s?

Q4. A particle in circular motion has a centripetal acceleration of \( 25 \, \text{m/s}^2 \) and radius \( 5 \, \text{m} \). What is its speed?

Q5. A stone is thrown horizontally at \( 7 \, \text{m/s} \) from a height of \( 31.25 \, \text{m} \). What is its time of flight? (Take \( g = 10 \, \text{m/s}^2 \))

Q6. In projectile motion, what is the angle between the velocity and acceleration vectors at the highest point?

Q7. A stone is dropped from a height of \( 20 \, \text{m} \) with a horizontal speed of \( 10 \, \text{m/s} \). What is its horizontal distance from the drop point when it lands? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. In motion with constant acceleration in a plane, what determines the path of the object?

Q9. For an object in projectile motion, which component of acceleration is zero?

Q10. A particle completes 5 revolutions in \( 2 \, \text{s} \) in a circular path of radius \( 0.8 \, \text{m} \). What is its linear speed?