NEET Motion in a Plane — Set 9

Question 1

A projectile is launched at $ 50 \, \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 = 50 \, \text{m/s}, \cos 37^\circ = 0.8 $. $ v_x = 50 \times 0.8 = 40 \, \text{m/s} $.

Question 2

In projectile motion, at what point is the speed of the projectile minimum?

Accepted Answer

The speed of a projectile is minimum at its maximum height because the vertical component of velocity ($ v_y $) is zero, leaving only the horizontal component ($ v_x $), which is constant. At all other points, the speed includes both components.

Question 3

A projectile is launched at $ 50 \, \text{m/s} $ at $ 60^\circ $. What is its range? (Take $ g = 10 \, \text{m/s}^2, \sin 60^\circ = 0.866 $)

Accepted Answer

Range $ R = \frac{v_0^2 \sin 2\theta_0}{g} $, where $ 2\theta_0 = 120^\circ, \sin 120^\circ = 0.866 $. Given: $ v_0 = 50 \, \text{m/s}, g = 10 \, \text{m/s}^2 $. $ R = \frac{50^2 \times 0.866}{10} = \frac{2500 \times 0.866}{10} = 216.5 \, \text{m} $.

NEET Physics: Motion in a Plane — Practice Set 9

Q1. A projectile is launched at \( 50 \, \text{m/s} \) at \( 37^\circ \). What is its speed at maximum height? (Take \( g = 10 \, \text{m/s}^2, \cos 37^\circ = 0.8 \))

Q2. In projectile motion, at what point is the speed of the projectile minimum?

Q3. A projectile is launched at \( 50 \, \text{m/s} \) at \( 60^\circ \). What is its range? (Take \( g = 10 \, \text{m/s}^2, \sin 60^\circ = 0.866 \))

Q4. A projectile is launched with a speed of \( 25 \, \text{m/s} \) at an angle of \( 37^\circ \) to the horizontal. What is the time taken to reach its maximum height? (Take \( g = 10 \, \text{m/s}^2 \), \( \sin 37^\circ = 0.6 \))

Q5. In uniform circular motion, what is the relationship between centripetal force and the object’s mass?

Q6. A projectile is launched at \( 45 \, \text{m/s} \) at \( 60^\circ \). What is its speed at the maximum height? (Take \( g = 10 \, \text{m/s}^2, \cos 60^\circ = 0.5 \))

Q7. A projectile is launched at \( 35 \, \text{m/s} \) at \( 60^\circ \). What is its range? (Take \( g = 10 \, \text{m/s}^2, \sin 120^\circ = 0.866 \))

Q8. What is the nature of the acceleration in uniform circular motion?

Q9. A ball is thrown horizontally at \( 9 \, \text{m/s} \) from a height of \( 44.1 \, \text{m} \). What is its speed on hitting the ground? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q10. What is the primary reason a projectile follows a curved path?