A mountain climber stands at the top of a 240m cliff that ov

A mountain climber stands at the top of a 24.0-m cliff that overhangs a calm pool of water. She throws two stones vertically 1.00 s apart and observes that they cause a single splash. The first stone had an initial velocity of -3.00 m/s. (Indicate the direction with the sign of your answers.) (a) How long after release of the first stone did the two stones hit the water? s (b) What initial velocity must the second stone have had, given that hit the water simultaneous? m/s (c) What was the velocity of each stone at the instant it hit water? first stone m/s second stone m/s A stuntman sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse 15.0 m/s, and the man is initial 2.45 m above the level of the saddle. (a) What must be the horizontal distance between the saddle and limb when the man makes his move? m

Solution

Here ,

u1 = -3 m/s

h = 24 m

a) time taken for stone 1 to reach ground is t1

-24 = -3 * t1 -0.5 * 9.8 * t1^2

solving for t1

t1 = 1.93 s

hence , they hit the water 1.93 s later

b)

let the initial speed of second stone is u2

-24 = u2 * ((1.93 - 1)) - 0.5 * 9.8 * (1.93 - 1)^2

u2 = -21.25 m/s

the speed of second stone must be - 21.25 m/s
c)

at the instant they hit water

velocity of first stone = -3 - 1.93 * 9.8

velocity of first stone = -21.91 m/s

for the stone 2 ,

velocity of second stone = -21.25 - 9.8 * 0.93

velocity of second stone = -30.26 m/s