A skydiver jumps out of a ;lane 3 km in the air and reaches terminal velocity after falling for 15 seconds. If he falls at a constant speed the rest of the way to the ground, how long will he have been in the air total?
I don't think it can be solved unless you consider what the friction was as it started to fall, it obviously was not falling that initial period at the rate of g.
To find out the total time the skydiver will have been in the air, we need to determine the time it takes for him to reach the ground after reaching terminal velocity.
The skydiver reaches terminal velocity after falling for 15 seconds. Terminal velocity is the point at which the force of gravity pulling the skydiver downwards is balanced by the upward force of air resistance. At this point, the skydiver falls at a constant speed.
To find the distance the skydiver falls to reach the ground after reaching terminal velocity, we can use the formula for distance traveled:
distance = speed × time
Since the skydiver falls at a constant speed after reaching terminal velocity, we can use the formula to calculate the distance traveled after reaching terminal velocity:
distance = speed × time
We know the distance from the plane to the ground is 3 km (3000 meters), and the skydiver has already fallen for 15 seconds.
Now, to calculate the time it takes for the skydiver to reach the ground after reaching terminal velocity, we rearrange the formula above:
time = distance / speed
Substituting the known values into the formula, we have:
time = 3000 meters / speed
Since we know the time it takes for the skydiver to reach terminal velocity (15 seconds), we can substitute it into the equation:
time = 3000 meters / speed
Now, we need to find the speed at which the skydiver falls at terminal velocity. Terminal velocity for a skydiver is typically around 53 meters per second.
Plugging in the known values, we have:
time = 3000 meters / 53 meters per second
Simplifying this gives us:
time ≈ 56.60 seconds
Therefore, the skydiver will have been in the air for a total of approximately 71.60 seconds (15 seconds to reach terminal velocity + 56.60 seconds in constant speed free fall).