Standing On The Shoulders Of Giants - Time Taken To Fall

Those who got it wrong are likely to have chosen 4. We know that the height of the tower is 56 (see previous question), and that it took at most 4 seconds to drop all the way. However, this does not imply that it took (close to) 4 seconds to reach the ground.

---

Solution: Acceleration due to gravity is a constant, and hence we get that $d(t) = A t^2$ , for some constant $A$ , as long as the object is still falling. Looking at $d(3)$ , a good approximation for $A$ is $\frac{ 44}{9}$ . Hence, we want to solve $56 = \frac{44}{9} T^2 \Rightarrow T = 3.38$ . As such, we choose the value of 3.5.

---

Of course, if you know that gravitational acceleration is $9.81 m/s^2$ , then you know that $d(t) = 4.9 t^2$ , which is what we used to model the distance traveled (with slight rounding).