After deploying her parachute, a skydiver falls through the air with a constant speed of 7.00 m/s . As she falls, there is a constant breeze blowing west at 4.50 m/s
If the skydiver deploys her parachute when she is 1100 m directly above her desired landing spot, by what distance will she miss that landing spot?
Well, I hope she packed a sense of direction along with her parachute! Let's do some math to find out the distance she'll miss her landing spot.
First, let's find out how long it takes for her to descend before deploying her parachute. We can use the equation:
distance = speed × time
The distance she needs to descend is 1100 m, and her constant speed is 7.00 m/s. So, we have:
1100 m = 7.00 m/s × time
Solving for time:
time = 1100 m / 7.00 m/s
time ≈ 157.14 seconds
Now let's find out how far she gets blown off course by the wind during this time. The wind is blowing west at a constant speed of 4.50 m/s. So we have:
distance blown off course = speed of wind × time
distance blown off course = 4.50 m/s × 157.14 seconds
distance blown off course ≈ 706.71 meters
Therefore, the skydiver will miss her landing spot by approximately 706.71 meters. Hope she doesn't mind a little detour!
To calculate the distance the skydiver will miss her landing spot, we need to consider the horizontal displacement caused by the wind.
Since the skydiver falls with a constant speed of 7.00 m/s, her vertical velocity is constant. Therefore, we can determine the time it takes for her to reach the ground by dividing the distance of 1100 m by her vertical velocity of 7.00 m/s.
Time = Distance / Velocity
Time = 1100 m / 7.00 m/s = 157.14 s
During this time, the wind blows westwards at a constant speed of 4.50 m/s. To calculate the horizontal displacement caused by the wind, we need to multiply the wind velocity by the time taken.
Horizontal Displacement = Wind Velocity * Time
Horizontal Displacement = 4.50 m/s * 157.14 s = 706.93 m
Therefore, the skydiver will miss her landing spot by a distance of approximately 706.93 meters.