NEET Motion in a Plane — Set 16

Question 1

A projectile is launched with a speed of 30 m/s at 30°. What is its horizontal velocity component?

Accepted Answer

Horizontal velocity v_x = v₀ cos θ₀. Given: v₀ = 30 m/s, cos 30° = √3/2. v_x = 30 × (√3/2) = 15 √3 ≈ 25.98 m/s.

Question 2

In uniform circular motion, what is true about the work done by the centripetal force?

Accepted Answer

The centripetal force is always perpendicular to the velocity (tangential) in uniform circular motion. Since work is the dot product of force and displacement, and the displacement is along the velocity, the work done is zero (force and displacement are perpendicular).

Question 3

A projectile is launched at $ 50 \, \text{m/s} $ at $ 53^\circ $. What is its speed at maximum height? (Take $ g = 10 \, \text{m/s}^2, \cos 53^\circ = 0.6 $)

Accepted Answer

At maximum height, speed = $ v_x = v_0 \cos \theta_0 $. Given: $ v_0 = 50 \, \text{m/s}, \cos 53^\circ = 0.6 $. $ v_x = 50 \times 0.6 = 30 \, \text{m/s} $.

NEET Physics: Motion in a Plane — Practice Set 16

Q1. A projectile is launched with a speed of 30 m/s at 30°. What is its horizontal velocity component?

Q2. In uniform circular motion, what is true about the work done by the centripetal force?

Q3. A projectile is launched at \( 50 \, \text{m/s} \) at \( 53^\circ \). What is its speed at maximum height? (Take \( g = 10 \, \text{m/s}^2, \cos 53^\circ = 0.6 \))

Q4. A projectile is launched at \( 22 \, \text{m/s} \) at \( 30^\circ \). What is its horizontal velocity component?

Q5. A boat sails east at \( 8 \, \text{m/s} \) while a current flows north at \( 6 \, \text{m/s} \). What is the magnitude of the boat’s velocity relative to the ground?

Q6. For an object in uniform circular motion, what happens if the centripetal force suddenly disappears?

Q7. A particle in uniform circular motion has a radius of \( 10 \, \text{m} \) and completes 4 revolutions in \( 8 \, \text{s} \). What is its centripetal acceleration?

Q8. A projectile is launched at \( 16 \, \text{m/s} \) at \( 60^\circ \). What is its time to reach maximum height? (Take \( g = 10 \, \text{m/s}^2, \sin 60^\circ = 0.866 \))

Q9. A stone is thrown horizontally at \( 20 \, \text{m/s} \) from a height of \( 45 \, \text{m} \). What is its time of flight? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A ball is projected with a speed of \( 28 \, \text{m/s} \) at an angle of \( 45^\circ \) to the horizontal. What is the maximum height attained? (Take \( g = 9.8 \, \text{m/s}^2 \))