Question

A grasshopper jumps straight up at 5.33m/s. How much time does it take for it to return to earth?

Answer 1

Use this kinematic equation to solve your question
\(\Delta x = \frac{1}{2}a t^2 + v_0 t\)
Where
a = -g = -9.8 m/s^2
\(v_0\) = 5.33 m/s

What do you think \(\Delta x\) will be? What is our displacement if we throw the ball straight up and want to know how long it takes to return to Earth?

Answer 2

Here, use the simplest equation of motion, \(v = u + at \), and **symmetry** - ie it will spend the same amount of time rising as it will falling back to earth.

So if the first leg, from ground to top of flight, takes time t', then using that equation:

\(0 = 5.33 + (-9.81) t' \implies t' = {5.33 \over 9.81}\)

Therefore, total flight time, \(t = 2 t' = 2 \cdot {5.33 \over 9.81}\)

Look at all the equations of motion before deciding which one to use, as judicious choice can simplify and save time.

Answer 3

That's another way to solve it.
The equation he used is \( v = v_0 + at\)
The initial velocity \( v_0\) of it as it rises is 5.33.
The final velocity when it reaches its maximum height will be 0. And then you can solve for time. And you multiply that time by 2 because it takes the same amount of time to come back down.