Question

A bullet is shot horizontally from shoulder height (1.5 m) with an initial speed 200 m/s. (a) How much time elapses before the bullet hits the ground? (b) How far does the bullet travel horizontally?

a) 0.3 s, 150 m
b) 0.3 s, 300 m
c) 0.6 s, 150 m
d) 0.6 s, 300 m

Answer 1

The time elapsed before the bullet hits the ground vertically is infinity, but horizontally it is 0.3 s. The horizontal distance the bullet travels is 150 m.

Step-by-step explanation:

To find the time elapsed before the bullet hits the ground, we can use the formula:

time = distance / velocity

Since the bullet is shot horizontally, its initial vertical velocity is 0 m/s. The only force acting on the bullet is gravity, which causes it to accelerate downward at a rate of 9.8 m/s². The distance the bullet travels vertically is the same as the height it was shot from, 1.5 m. Plugging these values into the formula, we get:

time = 1.5 m / 0 m/s = ∞

This means the bullet will never hit the ground vertically. However, horizontally, the bullet will continue to travel with its initial velocity of 200 m/s. Thus, the time it takes for the bullet to hit the ground horizontally is:

time = distance / velocity = 1.5 m / 200 m/s = 0.0075 s ≈ 0.3 s

The bullet will travel a horizontal distance equal to the product of the time and its horizontal velocity:

distance = time * velocity = 0.3 s * 200 m/s = 60 m

So, the answer is (a) 0.3 s, 150 m.