Considering the wasp aims to eat the fly, we assume the fly and wasp are one body after the collision. This is an inelastic collision. We can solve this with conservation of momentum.

 or 

For the two body inelastic colision between the wasp and the fly, we can rewrite this as:

Then taking into account the fact the fly is stationary initially:

Then solve for the velocity of the fly and the wasp after the collision:

This is a simple question of rate, time, and distance. 

, where  is distance travelled,  is rate,  is time passed. 

In our case, we know the rate  is 

We also know that the person travelled to  having originally started at  at . Keeping this in mind, the distance travelled is:

Now we just solve for time:

In this question, we're being asked to determine how long a ball will remain in the air when it is thrown vertically upward on a planet with reduced gravity. First, we'll need to find an expression that relates gravity with the amount of time the ball remains in the air. To do this, we can make use of the kinematics equations.

Furthermore, since we know the ball will land where it began, we know that .

Moreover, if we define the upward direction as positive and the downward direction as negative, then we know that , since gravity is always pointing in the downward direction.

The above expression is the one we're looking for because it relates time and gravity. From this expression, we can conclude that if the magnitude of gravity is reduced by a factor of three, then the time variable will increase by a factor of three.

In this problem, we're told that a uniformly accelerating car travels a certain distance in a given amount of time, and we're asked to solve for the acceleration.

For starters, it's important to notice that the car is undergoing uniform acceleration. This means that the car's acceleration is constant, which is important because it means we can utilize the kinematic equations. For this problem, we'll need to use an equation that relates displacement, time, and acceleration.

Because the car is initially starting at rest, we can set the  term equal to zero.

To solve this problem we look to the kinematic equations. Based on our need to include distance there are only two equations that might work and since we only know the initial speed we will use:

Because gravity is the only force acting to slow her upward rise we can find the time:

Looking at the initial information we are given about the particle at , we can construct the equation of motion for the position of the particle as:

Plug in our values and solve.

We begin by noting we have been given no information about the time in which the stopping is to occur, only velocities and distance. This points us to the following kinematic equation:

By using the given information, and noting that coming to a stop implies a final velocity of , we can directly substitute the numbers in and solve. It makes sense the final value is negative because the car is being accelerated in the negative direction in order to stop it.

A tailwind is a wind traveling in the same direction as an object. The find the new speed of the airplane, we add the speed of the tailwind to the speed of the airplane.

Using the following kinematic equation:

 is the final position, in meters, ( for ground).

 is the starting position ( above ground)

 is the starting velocity   because the ball is dropped and therefor starts from rest).

 is the acceleration due to gravity given by the problem statement.

Input these values into the first ruling equation and note that in this notation up is the positive direction so the acceleration due to gravity is negative:

Then we solve for .

We use the equation:

With , , , and  we have:

The bag has fallen 39 meters from its original position. Note that the question does not ask for the distance the bag is from the basket after 3 seconds so we do not have to take in to account how far the balloon has moved in the 3 seconds. Also, note that the question asks "how far" the bag is from the basket, so we do not have to worry about sign in the answer.