A cricket ball is thrown at speed of 28 ms in direction 30° above the horizontal. Calculate the time taken by the ball to return the same level.

The correct answer is 2) 2.9 s.

Key Points

• The time of flight of a projectile is given by the formula: T = (2u sin θ) / g, where u is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity (9.8 m/s²).
• Here, the initial speed (u) = 28 m/s, and the angle (θ) = 30°.
• Using the sine of 30°, which is 0.5, the formula becomes: T = (2 × 28 × 0.5) / 9.8 = 2.857 seconds.
• Rounding to one decimal place, the time of flight is approximately 2.9 seconds.
• This calculation assumes no air resistance and that the projectile lands at the same level from which it was thrown.

Additional Information

• Time of Flight: The total time taken by a projectile to return to the same vertical level from which it was projected.
• Key Formula for Projectile Motion: The motion of a projectile is analyzed using these equations:
  • Horizontal Range: R = (u² sin 2θ) / g
  • Maximum Height: H = (u² sin²θ) / (2g)
  • Time of Flight: T = (2u sin θ) / g
• Acceleration due to Gravity (g): On Earth, the standard value of g is approximately 9.8 m/s², which influences the motion of all freely falling objects.
• Angle of Projection: The angle at which an object is projected determines its trajectory and the distance it covers. For maximum range, the optimal angle is 45°.
• Sine and Cosine Functions: In trigonometry, these functions are crucial for resolving a vector into its horizontal and vertical components. For θ = 30°, sin 30° = 0.5 and cos 30° = √3/2.