NEET Motion in a Plane — Set 17

Question 1

What is the primary factor affecting the time of flight of a projectile launched from level ground?

Accepted Answer

The time of flight of a projectile depends on the initial vertical velocity component ($ v_0 \sin \theta_0 $) and gravity ($ g $), as given by $ T_f = \frac{2 v_0 \sin \theta_0}{g} $. The vertical component determines how long the projectile stays in the air.

Question 2

A ball is thrown horizontally at $ 6 \, \text{m/s} $ from a height of $ 4.9 \, \text{m} $. What is its horizontal range? (Take $ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

Time to fall: $ h = \frac{1}{2} g t^2 \Rightarrow 4.9 = \frac{1}{2} \times 9.8 \times t^2 \Rightarrow 4.9 = 4.9 t^2 \Rightarrow t^2 = 1 \Rightarrow t = 1 \, \text{s} $. Horizontal range $ R = v_x t = 6 \times 1 = 6 \, \text{m} $.

Question 3

For a projectile launched at an angle, what is true about the horizontal and vertical motions?

Accepted Answer

The horizontal and vertical motions in projectile motion are independent of each other. The horizontal motion is uniform (constant velocity), while the vertical motion is uniformly accelerated due to gravity, allowing separate analysis of each component.

NEET Physics: Motion in a Plane — Practice Set 17

Q1. What is the primary factor affecting the time of flight of a projectile launched from level ground?

Q2. A ball is thrown horizontally at \( 6 \, \text{m/s} \) from a height of \( 4.9 \, \text{m} \). What is its horizontal range? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q3. For a projectile launched at an angle, what is true about the horizontal and vertical motions?

Q4. A particle moves in a circular path of radius \( 3 \, \text{m} \) with a speed of \( 6 \, \text{m/s} \). What is its angular speed?

Q5. In projectile motion, what is conserved throughout the trajectory if air resistance is negligible?

Q6. A stone is dropped from a cliff 45 m high with an initial horizontal speed of 15 m/s. What is its speed on hitting the ground? (Take g = 10 m/s²)

Q7. A particle starts from rest with an acceleration of \( (4 \hat{i} + 3 \hat{j}) \, \text{m/s}^2 \). What is its displacement magnitude after \( 2 \, \text{s} \)?

Q8. What is the physical significance of the time of flight being zero for a projectile?

Q9. A particle moves in a circle of radius \( 1.5 \, \text{m} \) with a speed of \( 3 \, \text{m/s} \). What is its centripetal acceleration?

Q10. A particle’s position is given by \( x = 2t^2 + 3t \) and \( y = t^2 - 2t \) (in meters and seconds). What is the magnitude of its velocity at \( t = 2 \, \text{s} \)?