NEET Motion in a Plane — Set 7

Question 1

For an object moving in a plane with constant acceleration, what is true about its velocity vector?

Accepted Answer

In motion with constant acceleration in a plane, the velocity vector changes in magnitude and/or direction over time because the acceleration continuously alters it. Unlike uniform motion, the velocity is not constant unless the acceleration is zero.

Question 2

A projectile is launched at $ 15 \, \text{m/s} $ at $ 30^\circ $. What is its time of flight? (Take $ g = 10 \, \text{m/s}^2, \sin 30^\circ = 0.5 $)

Accepted Answer

Time of flight $ T_f = \frac{2 v_0 \sin \theta_0}{g} $. Given: $ v_0 = 15 \, \text{m/s}, \sin 30^\circ = 0.5, g = 10 \, \text{m/s}^2 $. $ T_f = \frac{2 \times 15 \times 0.5}{10} = \frac{15}{10} = 1.5 \, \text{s} $.

Question 3

A stone is thrown horizontally at $ 10 \, \text{m/s} $ from a height of $ 80 \, \text{m} $. What is its time of flight? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Vertical motion: $ y = \frac{1}{2} g t^2 $, where $ y = -80 \, \text{m} $. $ -80 = \frac{1}{2} \times 10 \times t^2 \Rightarrow -80 = 5 t^2 \Rightarrow t^2 = 16 \Rightarrow t = 4 \, \text{s} $.

NEET Physics: Motion in a Plane — Practice Set 7

Q1. For an object moving in a plane with constant acceleration, what is true about its velocity vector?

Q2. A projectile is launched at \( 15 \, \text{m/s} \) at \( 30^\circ \). What is its time of flight? (Take \( g = 10 \, \text{m/s}^2, \sin 30^\circ = 0.5 \))

Q3. A stone is thrown horizontally at \( 10 \, \text{m/s} \) from a height of \( 80 \, \text{m} \). What is its time of flight? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. In projectile motion, what is the condition for achieving maximum horizontal range on level ground?

Q5. A particle starts from rest with an acceleration of \( (3 \hat{i} + 5 \hat{j}) \, \text{m/s}^2 \). What is its displacement magnitude after \( 2 \, \text{s} \)?

Q6. What is the significance of the horizontal component of velocity in determining the range of a projectile?

Q7. A ball is thrown horizontally at \( 12 \, \text{m/s} \) from a height of \( 24.5 \, \text{m} \). What is its horizontal range? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q8. A projectile is launched with a speed of \( 15 \, \text{m/s} \) at an angle of \( 60^\circ \) to the horizontal. What is its maximum height? (Take \( g = 10 \, \text{m/s}^2, \sin 60^\circ = 0.866 \))

Q9. A swimmer moves north at \( 3 \, \text{m/s} \) in a river flowing west at \( 4 \, \text{m/s} \). What is the magnitude of the swimmer’s velocity relative to the ground?

Q10. In projectile motion, what is true about the total mechanical energy, assuming no air resistance?