What difference is there between the downward velocities of the skydiver who jumped out of the helicopter (with no forward velocity) and the one who jumped out of a plane (with a forward velocity of 40 m/s)?
When forward velocity is 40 m/s, the downward velocity is zero.
To understand the difference in downward velocities between the two scenarios, we need to consider the concept of relative velocities.
When a skydiver jumps out of a helicopter with no forward velocity, their initial downward velocity is entirely due to the force of gravity pulling them down. In this case, the skydiver's downward velocity can be determined using the equations of motion and the acceleration due to gravity (approximately 9.8 m/s²). The exact value will depend on factors such as the skydiver's body position and air resistance.
On the other hand, when a skydiver jumps out of a plane with a forward velocity of 40 m/s, we need to consider both the downward velocity due to gravity and the horizontal velocity due to the forward motion of the plane. In this scenario, the skydiver's downward velocity will be the vector sum of the downward component due to gravity and the downward component caused by the horizontal motion.
To calculate the downward velocity, we'll need to decompose the 40 m/s horizontal velocity into its vertical and horizontal components. The upward component will cancel out the downward gravitational force to some extent. Then, we can find the resultant or net downward velocity by adding the remaining downward component due to gravity to the upward component from the horizontal velocity.
In summary, the skydiver who jumps out of the helicopter will have a downward velocity solely due to gravity. However, the skydiver who jumps out of the plane with a forward velocity of 40 m/s will have a resultant downward velocity caused by a combination of the force of gravity and the horizontal motion of the plane.
To compare the downward velocities of the two skydivers, we need to consider the effect of air resistance. Assuming everything else is the same (e.g., mass, size, body position), the skydiver who jumped out of the plane with a forward velocity of 40 m/s will have a lower downward velocity compared to the skydiver who jumped out of the helicopter with no forward velocity.
This is because the forward velocity of the skydiver who jumped out of the plane will cause a greater amount of air resistance or drag. As the skydiver moves forward, the air molecules collide with their body, exerting a force that opposes the motion. This force of air resistance increases with velocity.
As a result, the skydiver with a forward velocity will experience a greater opposing force due to air resistance than the skydiver with no forward velocity. This increase in air resistance will lead to a downward velocity that is lower than the skydiver who jumped out of the helicopter. However, it is important to note that the actual values of the downward velocities will depend on various factors such as the weight, body position, and the specific design of the parachute used.