Question

1.) A stone falls from rest from the top of a cliff.

A second stone is thrown downward from the
same height 2.2 s later with an initial speed of
43.12 m/s. They hit the ground at the same
time.
How long does it take the first stone to hit
the ground? The acceleration of gravity is
9.8 m/s^2.
Answer in units of s.

Answer for the first question is 3.3s. I just need the second one.

2.) How high is the cliff?
Answer in units of m

Answer 1

Step-by-step explanation:

ignore air resistance

Let t be the time of fall for the dropped stone.

½(9.8)t² = 43.12(t - 2.2) + ½(9.8)(t - 2.2)²

4.9t² = 43.12t - 94.864 + 4.9(t² - 4.4t + 4.84)

4.9t² = 43.12t - 94.864 + 4.9t² - 21.56t + 23.716

0 = 21.56t - 71.148

t = 71.148/21.56 = 3.3 s

h = ½(9.8)3.3² = 53.361 = 53 m

or

h = 43.12(3.3 - 2.2) + ½(9.8)(3.3 - 2.2)² = 53.361 = 53 m