NEET Motion in a Plane — Set 13

Question 1

A projectile is launched at $ 24 \, \text{m/s} $ at $ 60^\circ $ to the horizontal. What is its time of flight? (Take $ g = 9.6 \, \text{m/s}^2, \sin 60^\circ = 0.866 $)

Accepted Answer

Time of flight $ T_f = \frac{2 v_0 \sin \theta_0}{g} $. Given: $ v_0 = 24 \, \text{m/s}, \sin 60^\circ = 0.866, g = 9.6 \, \text{m/s}^2 $. $ T_f = \frac{2 \times 24 \times 0.866}{9.6} = \frac{41.568}{9.6} \approx 4.33 \, \text{s} $.

Question 2

A projectile is launched at $ 40 \, \text{m/s} $ at $ 37^\circ $. What is its speed at maximum height? (Take $ g = 10 \, \text{m/s}^2, \cos 37^\circ = 0.8 $)

Accepted Answer

At maximum height, speed = $ v_x = v_0 \cos \theta_0 $. Given: $ v_0 = 40 \, \text{m/s}, \cos 37^\circ = 0.8 $. $ v_x = 40 \times 0.8 = 32 \, \text{m/s} $.

Question 3

A ball is thrown horizontally at $ 11 \, \text{m/s} $ from a height of $ 19.6 \, \text{m} $. What is its speed on hitting the ground? (Take $ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

Vertical velocity: $ v_y = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 19.6} = \sqrt{384.16} \approx 19.6 \, \text{m/s} $. Horizontal velocity: $ v_x = 11 \, \text{m/s} $. Speed $ v = \sqrt{v_x^2 + v_y^2} = \sqrt{11^2 + 19.6^2} = \sqrt{121 + 384.16} = \sqrt{505.16} \approx 22.47 \, \text{m/s} $.

NEET Physics: Motion in a Plane — Practice Set 13

Q1. A projectile is launched at \( 24 \, \text{m/s} \) at \( 60^\circ \) to the horizontal. What is its time of flight? (Take \( g = 9.6 \, \text{m/s}^2, \sin 60^\circ = 0.866 \))

Q2. A projectile is launched at \( 40 \, \text{m/s} \) at \( 37^\circ \). What is its speed at maximum height? (Take \( g = 10 \, \text{m/s}^2, \cos 37^\circ = 0.8 \))

Q3. A ball is thrown horizontally at \( 11 \, \text{m/s} \) from a height of \( 19.6 \, \text{m} \). What is its speed on hitting the ground? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q4. What is the primary reason an object in uniform circular motion does not move towards the center?

Q5. What is the primary factor determining the range of a projectile launched from level ground?

Q6. A particle in circular motion has a centripetal acceleration of \( 64 \, \text{m/s}^2 \) and radius \( 4 \, \text{m} \). What is its speed?

Q7. For an object in uniform circular motion, what is the direction of its acceleration?

Q8. A stone is thrown horizontally at \( 14 \, \text{m/s} \) from a height of \( 39.2 \, \text{m} \). What is its time of flight? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q9. In projectile motion, what is the direction of acceleration throughout the trajectory?

Q10. An object completes 5 revolutions in 10 s in a circular path of radius 3 m. What is its linear speed?