Answer:
The projectile will it travel in 57.5 m in the x-direction if the cliff is 95 meters high. Option A is correct.
Step-by-step explanation:
Since the projectile is fired horizontally, its vertical velocity is initially zero. The only force acting on the projectile in the vertical direction is gravity, which will cause it to accelerate downward at a rate of 9.81 m/s². The time it takes for the projectile to fall to the ground can be calculated using the following equation:
h = 0.5 * g * t²
where:
- h is the height (95 meters)
- g is the acceleration due to gravity (9.81 m/s²)
- t is the time (in seconds)
Solving for t, we get:
t = √(2h / g) = √(2 * 95 / 9.81)
t = 4.6 seconds
During this time, the projectile will continue to move horizontally at a constant velocity of 40 m/s. The distance it travels in the x-direction can be calculated using the following equation:
d = v * t
where:
- d is the distance (in meters)
- v is the velocity (40 m/s)
- t is the time (4.6 seconds)
Solving for d, we get:
d = v * t
d = 40 * 4.6
d = 184 meters
However, this is the total distance traveled by the projectile in the x-direction. Since the cliff is 95 meters high, the projectile will need to travel back to the same height to fall to the ground. Therefore, the distance it travels in the x-direction before hitting the ground is:
d = 184 - 2 * 95
d = 57.5 meters
Therefore, the correct answer is A) 57.5 m.