Question

A bullet fired horizontally hits the ground in 0.5 sec. If it had been fired with a much higher speed in the same direction, and neglecting air resistance and the earth’s curvature, it would have hit the ground in1. There is no way to tell from the information given.
2. less than 0.5 sec.
3. 0.5 sec.
4. more than 0.5 sec.

Answer 1

Answer:

3. 0.5 sec.

Explanation:

A bullet fired horizontally follows a projectile motion, which consists of two independent motions:

- A horizontal motion with constant speed

- A vertical motion with  constant acceleration, g = 9.8 m/s^2, towards the ground

The time taken for the bullet to reach the ground can be calculated just by considering the vertical motion:

$y(t) = h + v_{0y} t - \frac{1}{2}gt^2$

where y is the vertical position at time t, h is the initial height, and $v_{0y}$ is the initial vertical velocity of the bullet.

Since the bullet is fired horizontally, $v_{0y}=0$. So the equation becomes

$y(t) = h - \frac{1}{2}gt^2$

And the time that the bullet takes to reach the ground can be found by requiring y=0 and solving for t:

$t=\sqrt{\frac{2h}{g}}$

As we can see, in this equation there is no dependance on the initial speed of the bullet: therefore, if the bullet is fired still horizontally but with a different speed, it will still take the same time (0.5 s) to reach the ground.