Acelebrated mark twain story has motivated contestants in the calaveras county jumping frog jubilee, where frogs jump as long as 2.2 m have been recorded. if a frog jumps 2.2 m and the launch angle is 45°, find (a) the frog’s launch speed and (b) the time the frog spends in the air. ignore air assistance.

Answers:

a) 6.566 m/s

b) 0.947 s

Explanation:

The frog's jump can be modeled as projectile motion and the main equations that will be useful in this situation are:  

  (1)  

  (2)  

Where:  

 is the height of the frog at a given time  

 is the initial height of the frog (assuming it has jumped from ground)

 is the launch speed (initial speed) of the frog

 is the angle at which the frog jumped

 is the time the frog spends on air during the whole parabolic movement

 is the acceleration due gravity

 is the final speed of the frog at a given time

Knowing this, let's begin with the answers:

In this case we will use equation (2) assuming the final velocity of the frog when it hits the ground is zero ():

  (3)  

Then we will isolate :

  (4)  

  (5)  

  (6)  This is the frog's launch speed

Since we already have the value of we can find the time the frog spends in the air with equation (1), which is fullfilled when :

  (7)  

Isolating :

  (8)  

  (9)  

Finally:

  (10)  This is the time the frog spends in the air

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