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:
<h2>(a) The frog’s launch speed </h2>
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
<h2>(b) The time the frog spends in the air</h2>
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