Final answer:
The horizontal distance a projectile travels when fired from a cliff can be found by calculating the time it takes to hit the ground using the formula for vertical displacement, and then using the constant horizontal velocity to find the horizontal distance.
Step-by-step explanation:
The student's question involves calculating the horizontal distance a projectile will travel when fired from a height. The object is fired horizontally at a velocity of 40 m/s from a cliff that is 95 meters high. In projectile motion, the horizontal and vertical motions are independent of each other, with the horizontal velocity remaining constant as the only acceleration acting on the projectile is due to gravity in the vertical direction.
To find out how far the projectile will travel in the x direction, we need to determine the time it takes for the object to reach the ground. Using the formula for vertical displacement s = ut + 0.5at2, where s is the vertical distance (95 m), u is the initial vertical velocity (0 m/s), a is the acceleration due to gravity (9.81 m/s2), and t is the time in seconds, we can solve for t. Since the projectile is fired horizontally, its initial vertical velocity is zero, simplifying the formula to s = 0.5at2. Solving for t, we get t = √(2s/a), which gives us the time taken to fall to the ground.
After calculating the time, we then use the horizontal velocity and time to find out the horizontal distance traveled: x = vt, where x is the horizontal distance and v is the horizontal velocity.