Monkey throws a banana horizontally from the top of a tree .the banana hits the ground 3 second later and 30 meter from the base of the
1. how fast did the monkey throw the banana?
2 .how tall is the tree?
3. how fast was the banana moving vertically as it hits the ground?

1).  Gravity has no effect on horizontal speed, which remains constant
(as long as we're ignoring air resistance.

So banana traveled 30 meters horizontally in 3 seconds.
Horizontal speed (speed of throw) is  10 m/s .


2). Distance fallen in free-fall is      (1/2) (G) (T²) .

'G' is 9.8 m/s² on Earth, and 'T' is 3 sec.

                 (1/2) (G) (T²) = (4.9 m/s²) (9 s²) =  44.1 meters .


3).  On Earth, acceleration of gravity is 9.8 m/s² .
That means that at any time during free-fall, the vertical speed
is 9.8 m/s faster than it was 1 second earlier.
Starting from zero vertical speed, the falling speed at the end
of 3 seconds is
                         (3 sec) x (9.8 m/s²) =  29.4 m/s .


4).  As the banana hits the ground, its velocity is

                    10 m/s horizontal  +  29.4 m/s vertical

               =  √(10² + 29.4²) = √964.36 
                   at an angle of  arctan(10/29.4) away from vertical

               =  31.05 m/s  at  18.8° away from vertical .  

The velocity is becoming closer and closer to vertical as time goes
on, because the horizontal component isn't changing, but the vertical
component is growing at the rate of 9.8 m/s per second.

 

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