Question

If an object were dropped from an airplane at normal gravity and no air resistance, how far would it need to travel before its speed is 145 m/s?

a) 132.25 meters
b) 162.25 meters
c) 126.25 meters
d) 156.25 meters

Answer 1

Using the kinematic equations, the distance an object would need to fall to reach a speed of 145 m/s from rest under gravity is calculated to be approximately 1071.44 meters, which is not listed among the choices provided.

Step-by-step explanation:

To determine how far an object would need to travel to reach a speed of 145 m/s when dropped from an airplane with no air resistance, we can use the equation for the distance traveled under the influence of gravity (d = ½ * g * t²), with g being the acceleration due to gravity (9.8 m/s²) and t being the time it takes to reach the speed. Since the object is accelerating uniformly, we can use the equation v = g * t to find the time it takes to reach 145 m/s. Solving for t gives us t = v / g = 145 m/s / 9.8 m/s² ≈ 14.8 s.

Now, we can determine the distance d using d = ½ * g * t² = ½ * 9.8 m/s² * (14.8 s)² ≈ 1071.44 m. This distance is far greater than the options given, indicating a potential error in the question or the options provided. However, as a thought experiment under ideal conditions, this would be the theoretical distance required.