Answer:
27.52 meters is the height of the cliff.
Explanation:
Second equation of motion:
\(h=u\times t+\frac{1}{2}g\times t^2\)
u = Initial velocity
t = Time taken to cover h distance
g = Acceleration due to gravity
Let the height of the cliff be h
Stone-1:
Initial velocity of the stone = u = 0 m/s
Time to cover h height of cliff, t = ?, g = \(9.8 m/s^2\)
\(h=0 m/s\times t+\frac{1}{2}g\times t^2\)..[1] (Second equation of motion)
Stone-2:
Initial velocity of the stone = u' = 32 m/s,
Time to cover h height of cliff = t' = (t-1.6),
g = \(9.8 m/s^2\)
\(h=32 m/s\times (t-1.6)+\frac{1}{2}g(t-1.6)^2\)..[2]
Both stones are covering same distance or height of the cliff: [1]= [2]
\(0 m/s\times t+\frac{1}{2}g\times t^2=32 m/s\times (t-1.6)+\frac{1}{2}g(t-1.6)^2\)
On solving for t:
t = 2.37 seconds
\(h=0 m/s\times 2.37 s+\frac{1}{2}g\times t^2=\frac{1}{2}\times 9.8 m/s^2\times (2.37 s)^2\)
h = 27.52 m
27.52 meters is the height of the cliff.
