An 8g bullet leaves a gun at 700ms-1.

(a) what is the maximum height that this bullet could reach (ignoring air resistance)

12500

To find the maximum height reached by the bullet, we can use the principles of projectile motion. Here's the step-by-step explanation of how to calculate it:

Step 1: Identify the relevant variables:
- Initial velocity (u) = 700 m/s (speed at which the bullet leaves the gun)
- Acceleration due to gravity (g) = 9.8 m/s² (assuming the bullet is fired on Earth's surface)

Step 2: Determine the time taken to reach maximum height:
The time taken to reach the maximum height can be found by dividing the initial vertical velocity by the acceleration due to gravity. Since the vertical initial velocity is 0 m/s (at maximum height), the calculations will look like this:

u = g * t
700 m/s = 9.8 m/s² * t

Solving for t:
t = 700 m/s / 9.8 m/s² ≈ 71.43 s (rounded to two decimal places)

Step 3: Calculate the maximum height (h):
Using the time calculated in step 2, we can find the maximum height reached by the bullet using the formula for height in projectile motion:

h = u * t - 0.5 * g * t²

Plugging in the values:
h = 700 m/s * 71.43 s - 0.5 * 9.8 m/s² * (71.43 s)²

Simplifying:
h ≈ 249500 m (rounded to three significant figures)

Therefore, the maximum height that the bullet could reach, ignoring air resistance, is approximately 249500 meters.