A hunter aims directly at a target (on the same level) 120 m away.?

(a) If the bullet leaves the gun at a speed of 250 m/s, by how much will it miss the target?

(b) At what angle should the gun be aimed so as to hit the target?

How long does it take for the bullet to go 120 meters?

How much does the bullet fall in that time?

b) tanTheta=falling distance/120

got it 1.13m and .54 degrees.

correct

To answer these questions, we need to break down the problem into different components.

(a) To find how much the bullet will miss the target, we need to calculate the horizontal displacement. Since we know the initial speed of the bullet and the distance to the target, we can use the equation:

Horizontal Displacement = Initial Speed × Time

In this case, the initial speed is 250 m/s, and the horizontal displacement is the distance to the target, which is 120 m. We can rearrange the formula to solve for time:

Time = Horizontal Displacement / Initial Speed

Plugging in the values, we get:

Time = 120 m / 250 m/s ≈ 0.48 s

Now, to find the horizontal displacement, we can use the formula:

Horizontal Displacement = Initial Speed × Time

Substituting the values we know:

Horizontal Displacement = 250 m/s × 0.48 s ≈ 120 m

Therefore, the bullet will not miss the target at all. It will hit the target dead on.

(b) Now, let's determine the angle at which the gun should be aimed to hit the target. To achieve that, we can calculate the vertical displacement and the time of flight for the bullet.

Vertical Displacement = 0 (Since the target and the gun are at the same height)

Time of Flight = 2 × Vertical Displacement / Acceleration

Acceleration due to gravity is approximately 9.8 m/s².

Substituting the values, we get:

0 = 2 × (-9.8 m/s²) × Time of Flight

Simplifying the equation:

Time of Flight = 0

This implies that the bullet will take no time to reach the target when fired horizontally. Therefore, the gun should be aimed horizontally, with no vertical angle, to hit the target.