a police shot a wall of 10 meter which is located 75 meter from himself. the angle between base and bullet was 60 degree and the speed was 30 meter per second was shot. was the bullet shot the wall ornot ..Explain if why?

To determine whether the bullet shot the wall or not, we can calculate the height the bullet reaches at a distance of 75 meters using basic trigonometry.

Given:
- Distance from the police officer to the wall (base) = 75 meters
- Angle between base and bullet (initial angle of elevation) = 60 degrees
- Speed of the bullet = 30 meters per second

First, we need to find the vertical component of the initial velocity of the bullet. We can find this by multiplying the speed of the bullet by the sine of the angle of elevation.

Vertical component of initial velocity = speed of bullet * sine(angle of elevation)
= 30 m/s * sin(60°)
≈ 30 m/s * 0.866
≈ 25.98 m/s

To calculate the time it takes for the bullet to reach the wall, we can use the formula:

Time = distance / horizontal velocity

The horizontal velocity can be found by multiplying the speed of the bullet by the cosine of the angle of elevation.

Horizontal component of initial velocity = speed of bullet * cosine(angle of elevation)
= 30 m/s * cos(60°)
≈ 30 m/s * 0.5
≈ 15 m/s

Time = 75 m / 15 m/s
= 5 seconds

Now, using the calculated time, we can determine the height the bullet reaches during this time using the vertical motion formula:

Final height = initial height + (initial vertical velocity * time) - (0.5 * acceleration * time^2)

Considering that there is no initial height (the bullet is fired from the ground) and there is no vertical acceleration, we can simplify the formula:

Final height = (initial vertical velocity * time)

Final height = 25.98 m/s * 5 s
= 129.9 meters

Since the height of the wall is given as 10 meters, and the calculated height reached by the bullet is approximately 129.9 meters, we can conclude that the bullet did not hit the wall.