A bridge is constructed above a river such that an object dropped from it will reach the river after 4.5 seconds. A precocious youth takes a small stone and throws it downwards with some negative inital velocity so that it hits the river afer only 3 seconds. With what final velocity will the thrown stone hit the water?

Vf = 11.04 m/s

Explanation:

First, we consider free fall motion with zero initial velocity. Using 2nd equation of motion:

h = Vi t + (1/2)gt²

where,

h = height of bridge = ?

Vi = Initial  Speed  = 0 m/s

t = time taken = 4.5 s

g = 9.8 m/s²

Therefore,

h = (0 m/s)(4.5 s) + (1/2)(9.8 m/s²)(4.5 s)²

Therefore,

h = 99.225 m

Now, we consider the forced motion when the youth throws the ball with some negative initial energy:

Vi = - Vi

t = 3 s

h = 99.225 m

Therefore,

99.225 m = - Vi(3 s) + (1/2)(9.8 m/s²)(3 s)²

Vi = (- 99.225 m + 44.145 m)/3 s

Vi = - 18.36 m/s

Now, we use this in 1st equation of motion for final velocity:

Vf = Vi + gt

Vf = -18.36 m/s + (9.8 m/s²)(3 s)

Therefore,

Vf = 11.04 m/s