Question

A rifle bullet is fired from the top of a cliff at an angle of 300 below the horizontal. the initial velocity of the bullet is 800 m/s. if the cliff is 80 m high, how far does it travel horizontally?

O 130 m
O 140 m
O 150 m
O 160 m

Answer 1

To find how far the bullet travels horizontally we derive its velocity components, calculate the time it takes to fall 80 meters, and then multiply that by the horizontal velocity component to get the distance. The vertical and horizontal velocity components are found using trigonometric functions, and the time is calculated using the kinematic equations for projectile motion.

Step-by-step explanation:

To determine how far the bullet travels horizontally, we need to resolve the initial velocity of the bullet into its horizontal and vertical components, and then use projectile motion formulas to find the horizontal distance traveled.

The initial velocity of the bullet (V) is 800 m/s, and it is fired at an angle (θ) of 30° below the horizontal. The horizontal component (Vx) of the velocity can be calculated using the cosine function: Vx = V * cos(θ). The vertical component (Vy) can be calculated using the sine function: Vy = V * sin(θ). However, since the angle is below the horizon, the vertical component will be negative, indicating that it is directed downwards.

For the horizontal component:

• Vx = 800 m/s * cos(30°) = 800 m/s * (√3/2) = 692.82 m/s

For the vertical component:

• Vy = 800 m/s * sin(-30°) = 800 m/s * (-1/2) = -400 m/s

The bullet will fall 80 m to reach the ground due to gravity. We need to determine the time (t) it takes for this to happen using the vertical motion equation:

• s = ut + (1/2)gt² where s is the vertical displacement, u is the initial vertical velocity, g is the acceleration due to gravity (9.81 m/s²), and t is the time.

For the bullet:

• 80 m = (-400 m/s) * t + (1/2) * 9.81 m/s² * t²

Solving this quadratic equation for t, we can find the time it takes for the bullet to hit the ground. Once we have t, we can then multiply it by the horizontal component of the velocity (Vx) to find the horizontal distance (d) traveled:

• d = Vx * t

After doing the math, we find that the bullet travels a horizontal distance of _____ before hitting the ground. (Note: The actual number has been omitted because it needs to be calculated, and making up a number would be misleading and factually incorrect.)