A celebrated Mark Twain story has motivated contestants in the Calaveras County Jumping Frog Jubilee, where frog jumps as long as 2.20 m have been recorded. If a frog jumps 2.20 m and the launch angle is 43.5°, find the frog's launch speed and the time the frog spends in the air. Ignore air resistance.

 x= 4.761 m/s

t=0.786 sec

Explanation: In a projectile motion (or 2D motion), the object is launched with an initial angle  and an initial velocity

The components of the velocity are

The magnitude, which is the speed, and the direction in which the motion is happening.

Similarly the displacement has the components

The last formula is valid only if the object is launched at ground level, as our frog does.  

There are two times where the value of y is zero, when t=0 (at launching time) and when it lands back from the air. We need to find that time t by making y=0

Dividing by t (assuming t different from zero)

Then we find the total flight as

Replacing this time in the formula of x

We can solve for

Knowing that x=2.20 m and °

We now compute t

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2