A bullet fired vertically upwards reaches a height of 500m. Neglecting air resistance, calculate the magnitude of the initial velocity of the bullet. [g = 1...

A bullet fired vertically upwards reaches a height of 500m. Neglecting air resistance, calculate the magnitude of the initial velocity of the bullet. [g = 10ms^-2]

Answer Details

When a bullet is fired vertically upwards, it will continue to move upward until the force of gravity acting downwards slows it down to a stop and then pulls it back down towards the ground. The maximum height the bullet reaches before it falls back down is called the maximum height or the vertex. At the maximum height, the final velocity of the bullet is zero, and the initial velocity is what we are required to find. We can use the equation of motion that relates the initial velocity, final velocity, acceleration and displacement to solve for the initial velocity. This equation is: v_f² = v_i² + 2as where v_f is the final velocity (zero), v_i is the initial velocity (what we want to find), a is the acceleration due to gravity (-10ms^-2 since it is acting in the opposite direction to the motion of the bullet), and s is the displacement (500m). Substituting the known values into the equation, we get: 0 = v_i² + 2(-10ms^-2)(500m) Simplifying, we get: v_i² = 10000 Taking the square root of both sides, we get: v_i = 100ms^-1 Therefore, the magnitude of the initial velocity of the bullet is 100.0ms^-1.