Physics Problem

Question

Two small frogs simultaneously leap straight up from a lily pad. Frog A leaps with an initial velocity of 0.726 m/s, while frog B leaps with an initial velocity of 1.62 m/s. When the first frog to return to the lily pad does so, what is the position and velocity of the other frog? Take upwards to be positive, and let the position of the lily pad be zero.

 

Position (m):

 

Velocity(m/s):

Answer 1

Hi Joey, 

 

I've subscribed to your question. 

 

I've written my answer as a series of hints, so you can try to use as few of them as possible. Stop reading if a hint gives you a big enough kick-start to finish the problem on your own.  If you have an attempt to show, I'd love to see it.

 

Hint 1:

 

Notice that the phrase "when the first frog to return to the lily pad does so" indicates a specific moment in time in a round-about way.  In order to evaluate the position and velocity of the other frog, we can take advantage that time is the common denominator here.  

 

Hint 2:

Both frogs pass through time at the same rate, and both frogs have kinematic equations that we can write in terms of time.

 

Hint 3: The frogs experience a constant acceleration of gravity throughout the motion.  

 

Hint 4: Thus if you can find a kinematic equation for the first frog that expresses its vertical displacement as a function of time, and set up that equation for the zero-displacement condition that the frog has while on the lily pad, you can solve for the value of time that makes the equation true.

 

Hint 5:  You should also be able to write kinematic equations for the displacement and velocity of the second frog, in terms of time, and by evaluating these at the (non-zero) time you solved for using the equation mentioned in hint 4,  determine both the rate at which the second frog is rising or falling and the displacement it is passing through at the moment the first frog lands.

 

If you have any more questions about this problem please let me know where you are getting stuck.