Question

A toy gun fires bullets in every possible direction. It is found that the bullet lands at a maximum horizontal distance of 6.4 m from the gun. Find the speed of projection (\( g = 10 \, \mathrm{m/s^2} \)).

Answer 1

Correct Answer: 8

Step 1: Understanding the Concept:
The maximum horizontal range of a projectile occurs when the angle of projection is \( 45^\circ \). The range formula is used to calculate the initial velocity.

Step 2: Key Formula or Approach:
Maximum Range: \( R_{max} = \frac{u^2}{g} \).

Step 3: Detailed Explanation:
Given \( R_{max} = 6.4 \, \text{m} \) and \( g = 10 \, \text{m/s}^2 \). \[ 6.4 = \frac{u^2}{10} \] \[ u^2 = 64 \] \[ u = \sqrt{64} = 8 \, \text{m/s} \]

Step 4: Final Answer:
The speed of projection is 8 m/s.