Question

Which of the following is the closest to the final velocity of the ball when it reaches the base of the hill, if the height of the hill is 2 meters?

(A) 0 m/s
(B) 1.4 m/s
(C) 2.8 m/s
(D) 4.2 m/s

Answer 1

Using the kinematic equation for free fall, the final velocity of a ball reaching the base of a 2-meter high hill is approximately 6.26 m/s. None of the provided options are correct for the given scenario.

Step-by-step explanation:

To solve for the final velocity of a ball when it reaches the base of the hill from a height of 2 meters, we can use the conservation of energy for a ball rolling down the hill without slipping or the kinematic equations for a ball sliding without friction. However, since the question does not specify whether the ball is rolling or sliding, we will assume it is in free fall. In that case, we can use the following kinematic equation derived from Newton's laws of motion:

v2 = u2 + 2as

Where v is the final velocity, u is the initial velocity (0 m/s since the ball is starting from rest at the top), a is the acceleration (9.8 m/s2 due to gravity), and s is the displacement (2 meters down the hill).

v2 = 0 + (2)(9.8 m/s2)(2 m) = 39.2 m2/s2

So,

v = sqrt(39.2 m2/s2)

Therefore, the final velocity v is approximately:6.26 m/s.

None of the given options (A) 0 m/s, (B) 1.4 m/s, (C) 2.8 m/s, nor (D) 4.2 m/s are correct.