Question

A cricmeter hits a ball with an initial velocity of 40 m/s. Calculate the maximum range.

• A. \( 80 \, \text{m} \)
• B. \( 160 \, \text{m} \)
• C. \( 200 \, \text{m} \)
• D. \( 320 \, \text{m} \)

Hint:

For maximum range, the optimal angle of projection is \( 45^\circ \), and the range depends on the square of the initial velocity divided by the gravitational constant.

Answer 1

The Correct Option is B

To calculate the maximum range \( R \) of a projectile, we use the formula: \[ R = \frac{v_0^2}{g} \sin(2\theta) \] where: - \( v_0 = 40 \, \text{m/s} \) (initial velocity) - \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity) - \( \theta = 45^\circ \) (optimal angle for maximum range) Since the angle for maximum range is \( 45^\circ \), \( \sin(90^\circ) = 1 \), so the formula becomes: \[ R = \frac{(40)^2}{9.8} = \frac{1600}{9.8} \approx 163.27 \, \text{m} \]
Thus, the maximum range is approximately \( 160 \, \text{m} \). Therefore, the correct answer is \( 160 \, \text{m} \).