Question

An object is dropped from a vertical distance of 31.7 m above the ground, and it takes 2.54 s to fall that distance. A second identical object is launched from the same height, with a horizontal velocity of 64.0 m/s. How long does the second object take to fall the 31.7 m?

Answer 1

The second object will take approximately 2.54 seconds to fall the 31.7 m.

Step-by-step explanation:

In this problem, we can use the concept of free fall to solve for the time it takes for the second object to fall a distance of 31.7 m. Since the object is launched horizontally with a velocity of 64.0 m/s, its vertical motion is independent of its horizontal motion. Therefore, the time it takes for the object to fall is the same as if it was dropped vertically from the same height. We can use the equation for free fall:

Distance = 0.5 * acceleration * time^2

where the acceleration due to gravity is approximately 9.8 m/s^2.

So, if we substitute the given values into the equation:

31.7 m = 0.5 * 9.8 m/s^2 * time^2

Solving for time:

time^2 = (31.7 m * 2) / (0.5 * 9.8 m/s^2)

time^2 = 6.46 s^2

time = √(6.46 s^2)

time ≈ 2.54 s

Therefore, the second object will take approximately 2.54 seconds to fall the 31.7 m.