Physics - Projectile Motion - Please Help!?

Question

A tiger leaps horizontally from a 12m high rock with a speed of 4.5m/s. How far from the base of the rock will she land?

and

A diver running 1.6 m/s dives out horizontally from the edge of a vertical cliff and reaches the water below at 3.0s later. How high ws the cliff and how far from its base did the diver hit the water?

Please show your work and explain to me how I can solve these two problems.

Answer 1

TIGER:

u=starting velocity, v=end velocity, t=time, a=acceleration=gravitational force= (10Nm^2)

Apply: S=ut+1/2at^2, for the vertical displacement:
12m = (0).t + 1/2 (10) t^2
12 = 5 t^2
t = Sqrt(12/5)

now apply the same formula for the horizontal displacement:
S=ut+1/2at^2
S= (vertical velocity) t + 1/2 (vertical acceleration) t^2
S= (4.5) t+ 1/2(0) t^2
S = 4.5 x sqrt(12/5) + 0
S = 6.97 metres
.
DIVER:
Apply vertically:(downwards)
S=ut+1/2at^2
S=(0). t+1/2(10)t^2
S = 5.(3)^2 = 45m
Height of cliff = 45m
.
Apply same formula horizontally:
s=ut+1/2at^2
S=(1.6).3 + 1/2(o).t^2
S= 4.8m

Answer 2

Both questions are of the same type, and can be solved using the same concepts. Something that makes them fairly simple is that the initial velocity is HORIZONTAL. Since there is no vertical component to the initial velocity, you can handle the vertical component of the object's path as if it the object were simply dropped.

First step:
Write the relationship between time and the distance the object has fallen. This is s = a t^2 / 2.
a is the acceleration of gravity: 9.8 m/s^2
t is the number of seconds since the object was dropped
s is the distance the object has fallen in t seconds

In the first example (the tiger), you know the value of s (4.5 m/s).
In the second example (the diver) you know the value of t (3.0 s).
In each case you know a (as mentioned above).
Use algebra to solve for the unknown value.

Second step:
You know how many seconds the object fell.
You know its horizontal velocity. The horizontal component is constant since there are no horizontal forces acting on the object (only the vertical force of gravity).
So you multiply the horizontal speed (in m/s) by the seconds that the object is in motion, and the result is the number of meters the object travels horizontally.

That's all you need to do.