Parachute but with no given mass.

[quiksilver2871]

Homework Statement

Parachutists open the canopy of their parachutes in order to reduce the speed at which
they land on Earth. How large should a parachute canopy be in order to reduce the
landing speed to 10 miles per hour? Consider the parachute to be circular, to be
descending vertically without gliding, and to have a coefficient of aerodynamic drag of
1.45

Homework Equations

problem is all equations i find include mass as a variable.

The Attempt at a Solution

none.

 

[Hootenanny]

Perhaps the mass will cancel out somewhere in the solution...?

 

[m2003]

I understand the importance of having all the necessary information in order to solve a problem accurately. In this case, the missing variable of mass makes it impossible to provide a specific answer to the question of how large the parachute canopy should be. The mass of the parachutist and other factors such as air resistance and gravitational force all play a crucial role in determining the appropriate size of the parachute canopy.

However, we can still discuss the general concept of how a parachute works to reduce landing speed. When a parachutist opens the canopy, it creates a larger surface area for the air to push against, which increases air resistance. This air resistance acts in the opposite direction of the force of gravity, slowing down the descent of the parachutist.

In order to achieve a landing speed of 10 miles per hour, the parachute canopy would need to provide enough air resistance to counteract the force of gravity acting on the parachutist. This would require a larger canopy size compared to a parachute used for a higher landing speed.

The coefficient of aerodynamic drag also plays a significant role in determining the size of the parachute canopy. A higher drag coefficient means that the canopy will experience more air resistance, resulting in a slower descent. In this case, the given coefficient of 1.45 suggests that the parachute canopy would need to be larger compared to a parachute with a lower coefficient.

In conclusion, while it is not possible to provide a specific answer without knowing the mass of the parachutist, we can still discuss the general principles involved in determining the appropriate size of a parachute canopy for a desired landing speed.