Question

A 20-pound object is dropped from a 50-foot bridge onto the ground below it. A 50-pound object is dropped from a 100-foot cliff onto the ground below it. Which object will hit the ground first?

Answer 1

The 50 pound object will reach the ground first.

Explanation:

Using the second equation of motion, we can derive the time taken for each of the object to reach the ground. As the object is thrown from the top of the bridge or cliff, acceleration due to gravity will be acting on them.

So, $s = ut+\frac{1}{2} at^{2}$

The value of s for the object thrown from 50 foot bridge is given as 50 ft. The initial velocity of the object will be zero. The acceleration can be written as the ratio of mass to gravitational force.

Then, $s = (0) t +\frac{1}{2}*\frac{m}{F}*t^{2}$

$50 = \frac{20}{2F} t^{2} \\\\t^{2} = \frac{100F}{20}$

$t = \sqrt{5F}$

Then, consider the time taken for the 50 pound object to reach the bottom of 100 ft cliff as t₁ and the displacement in this case is 100 ft.

Then, $100 = (0)t +\frac{1}{2}*\frac{50}{F}*t_{1}^{2} \\\\t_{1}^{2} =\frac{200F}{50}$

$t_{1} = 2 \sqrt{F}$

Since, the gravitational force acting on both the objects will be same, the ratio of time taken is

$\frac{t }{t_{1} }=\frac{\sqrt{5F} }{2\sqrt{F}} = \frac{\sqrt{5} }{2}$

So, the time taken for the 20 pound object to reach the ground of 50 ft bridge is √5 s =2.236 s and the time taken for the 50 pound object to reach the ground of 100 ft cliff is 2 s.

Thus, the 50 pound object will reach the ground first.