Final answer:
To calculate the time a bullet takes to hit the ground and its total velocity upon impact, we use the equations of projectile motion. The time is determined from the vertical distance and gravity, while the total velocity is the vector sum of the horizontal and vertical velocities just before impact.
Step-by-step explanation:
A bullet is fired horizontally at 300 m/s from a gun 1.5 m above the ground. When analyzing such a problem, we need to consider the projectile motion of the bullet, which involves both horizontal and vertical components of motion. Since the bullet is fired horizontally, the initial vertical velocity is zero.
- (a) To determine how long it takes for the bullet to return to the ground, we use the equation for the vertical motion under gravity, which is d = (1/2)gt² where d is the vertical distance (1.5 m), g is the acceleration due to gravity (9.81 m/s²), and t is the time in seconds. Solving this equation for t gives us the time it takes for the bullet to hit the ground.
- (b) The total velocity of the bullet just before it hits the ground will be the vector sum of the horizontal velocity (300 m/s) and the vertical velocity it has gained due to gravity. The horizontal velocity remains constant, but the vertical velocity can be determined using v = gt. The magnitude of the total velocity (hypotenuse) can then be calculated using the Pythagorean theorem, and the angle can be found using trigonometry.
Using the formulas mentioned above and the given initial conditions, we can solve for (a) the time taken for the bullet to hit the ground and (b) the components of total velocity at impact.