To solve this problem we use a kinematic equation that relates the square of the final velocity to the sum of the initial velocity squared and the change of position.

All values needed to find the final velocity are given, plug them in and solve.

The only force accelerating the object is gravity since it was dropped, not thrown. Thus, to find out the speed of the object after some time, simply multiply the time the object has fallen by the acceleration of gravity. We will use . Then use the average velocity to calculate the distance the phone fell.

Final velocity after 9s:

Distance the phone has fallen during the 9s of free fall:

Use a kinematic equation. Select the correct one by variables we have or do not have. We were given initial velocity, we know the final velocity will be zero because the orange has to hit the ground, and we know the acceleration of gravity. These parameters fit closest with the equation: 

Plug in the variables we know or were given:

Solve for vertical displacement:

Use a kinematic equation. Based on the variables we were given, the best equation to use is:

 and . We know initial velocity is 0 because it started from rest. Plug in known values:

The red term becomes 0.

Solve for horizontal displacement:

Based on the variables given select the appropriate kinematic equation. We only know gravity and time, but we need to solve for distance.

The red term becomes 0 because the rock was dropped. Its initial velocity is 0.

A person falling without air resistance only has the force of gravity acting on them. Thus, the acceleration of gravity multiplied by time yields the final speed of . The negative sign just indicates that the person is falling downward. 

We are given final velocity and we know initial velocity is 0. We can use the following kinematics formula to relate final speed, initial speed, acceleration, and displacement:

The red term is zero since Usain starts from rest. Plug in the remaining values and solve for acceleration. 

We were given final velocity and displacement and we know initial velocity is 0. Choose the following kinematics equation:

Initial velocity is zero and thus disappears from the equation. Plug in known values and solve for acceleration.

We know the final velocity, that initial velocity is 0, and the acceleration of the drone. We can find the time it takes to reach its takeoff speed by using the following kinematics formula:

The question asks to point out the false statement. Everything on Earth is accelerated downwards by gravity, all the time, by . Think of gravity as having a negative sign. When the ball is thrown up, acceleration is working against the velocity slowing the ball down. Their signs are opposite. But when the ball is falling back down to Earth, the velocity and acceleration have the same sign. So velocity and acceleration will not always have the same sign.

If gravity could be said to have a negative sign since it pulls everything downward, then an upward velocity would have a positive (and opposing sign). At the top of the trajectory when the ball's upward velocity is finally overcome by gravity, the sign of the velocity becomes negative as it now points back down to Earth. So it is true velocity changes sign at the top.

Since the ball is caught at the same height, both the time up and time down are equal and it will be traveling at the same speed. Since gravity is the only force acting on it, the ball loses all its velocity on the way up and regains that exact amount by the time it reaches the height it started the journey. This also makes the time up equal to the time it falls. If the same force acts with same strength (gravity) the entire time, why would either of these change?