Question

3. Newtonian mechanics demonstrates that the displacement of an object in free fall is given by the

relation s = ut + 1

2

at², where s is the displacement, u is the initial velocity, a is the acceleration, and t is the

time. This displacement equation is a polynomial expression. Polynomials enable people to describe the

physical world.

i. For example, assume that a ball is released from rest at the top of a building measuring 8.52 meters

tall. How long does it take for that ball to reach the ground?

(a) 1.23 seconds (b) 9.8 seconds (c) 1.32 seconds (d) 32 minutes

ii. Which is the true statement

(a) If time increases the displacement increases.

(b) If time decreases the displacement increases.

(c) Time is not changing, but displacement is happening.

(d) None of the above.​

Answer 1

Given: A ball is released from the top of a tower

           Height of tower = 8.52 m

To Find: Time taken by ball to reach the ground

              Correct statement in part ii.

Solution:

• For solving the first part of the question we will use the formula

                           s = ut + $\frac{1}{2}$at²                               (1)

where all notations are the same as given in the question.

• Negative value of s and g is taken due to direction from up to down.

Substituting the values given in (1)

                -8.52 = 0 × t + $\frac{1}{2}$(-10) t²      (when ball is dropped it is at rest initially)

           ⇒ -8.52 = -5 t²

           ⇒ t² = 1.704

           ⇒ t = √1.704 = 1.3 s

Therefore it takes the ball 1.3 s to reach the ground.

• For part ii., we will analyse equation (1) again.
• According to the equation, displacement is directly proportional to time, i.e, if time increases displacement will also increase.

Hence for part i. option (c) 1.32 s is the correct option and for part ii. option (a) If time increases the displacement increases is the correct option.